diff --git a/packages/doenetml-worker/src/components/BooleanInput.js b/packages/doenetml-worker/src/components/BooleanInput.js
index 49f428d9c..f7be01803 100644
--- a/packages/doenetml-worker/src/components/BooleanInput.js
+++ b/packages/doenetml-worker/src/components/BooleanInput.js
@@ -4,6 +4,7 @@ import {
     returnAnchorStateVariableDefinition,
 } from "../utils/graphical";
 import {
+    returnLabelAttributes,
     returnLabelStateVariableDefinitions,
     returnWrapNonLabelsSugarFunction,
 } from "../utils/label";
@@ -48,12 +49,6 @@ export default class BooleanInput extends Input {
             defaultValue: false,
             public: true,
         };
-        attributes.labelIsName = {
-            createComponentOfType: "boolean",
-            createStateVariable: "labelIsName",
-            defaultValue: false,
-            public: true,
-        };
         attributes.asToggleButton = {
             createComponentOfType: "boolean",
             createStateVariable: "asToggleButton",
@@ -73,6 +68,8 @@ export default class BooleanInput extends Input {
             forRenderer: true,
         };
 
+        Object.assign(attributes, returnLabelAttributes());
+
         Object.assign(attributes, returnAnchorAttributes());
 
         return attributes;
diff --git a/packages/doenetml-worker/src/components/CallAction.js b/packages/doenetml-worker/src/components/CallAction.js
index a4b94581c..68d8f7f9e 100644
--- a/packages/doenetml-worker/src/components/CallAction.js
+++ b/packages/doenetml-worker/src/components/CallAction.js
@@ -4,7 +4,10 @@ import {
     returnAnchorAttributes,
     returnAnchorStateVariableDefinition,
 } from "../utils/graphical";
-import { returnLabelStateVariableDefinitions } from "../utils/label";
+import {
+    returnLabelAttributes,
+    returnLabelStateVariableDefinitions,
+} from "../utils/label";
 import {
     addStandardTriggeringStateVariableDefinitions,
     returnStandardTriggeringAttributes,
@@ -56,13 +59,6 @@ export default class CallAction extends InlineComponent {
         // attributes.width = {default: 300};
         // attributes.height = {default: 50};
 
-        attributes.labelIsName = {
-            createComponentOfType: "boolean",
-            createStateVariable: "labelIsName",
-            defaultValue: false,
-            public: true,
-        };
-
         attributes.actionName = {
             createComponentOfType: "text",
             createStateVariable: "actionName",
@@ -78,6 +74,8 @@ export default class CallAction extends InlineComponent {
             forRenderer: true,
         };
 
+        Object.assign(attributes, returnLabelAttributes());
+
         Object.assign(attributes, returnAnchorAttributes());
 
         let triggerAttributes = returnStandardTriggeringAttributes(
diff --git a/packages/doenetml-worker/src/components/ChoiceInput.js b/packages/doenetml-worker/src/components/ChoiceInput.js
index 58d640de2..b25b00cbc 100644
--- a/packages/doenetml-worker/src/components/ChoiceInput.js
+++ b/packages/doenetml-worker/src/components/ChoiceInput.js
@@ -2,7 +2,10 @@ import Input from "./abstract/Input";
 import me from "math-expressions";
 import { enumerateCombinations, enumeratePermutations } from "@doenet/utils";
 import { setUpVariantSeedAndRng } from "../utils/variants";
-import { returnLabelStateVariableDefinitions } from "../utils/label";
+import {
+    returnLabelAttributes,
+    returnLabelStateVariableDefinitions,
+} from "../utils/label";
 
 export default class Choiceinput extends Input {
     constructor(args) {
@@ -102,12 +105,7 @@ export default class Choiceinput extends Input {
             fallBackToParentStateVariable: "submitLabelNoCorrectness",
         };
 
-        attributes.labelIsName = {
-            createComponentOfType: "boolean",
-            createStateVariable: "labelIsName",
-            defaultValue: false,
-            public: true,
-        };
+        Object.assign(attributes, returnLabelAttributes());
 
         return attributes;
     }
diff --git a/packages/doenetml-worker/src/components/Copy.js b/packages/doenetml-worker/src/components/Copy.js
index 6dec195c6..fc6ade24c 100644
--- a/packages/doenetml-worker/src/components/Copy.js
+++ b/packages/doenetml-worker/src/components/Copy.js
@@ -1830,6 +1830,7 @@ export default class Copy extends CompositeComponent {
             serializedReplacements = [
                 await replacementSourceComponent.serialize({
                     copyAll: !link,
+                    componentSourceAttributesToIgnore: ["labelIsName"],
                     copyVariants: !link,
                     primitiveSourceAttributesToIgnore: sourceAttributesToIgnore,
                     copyPrimaryEssential,
diff --git a/packages/doenetml-worker/src/components/Function.js b/packages/doenetml-worker/src/components/Function.js
index 9f8600206..7782141aa 100644
--- a/packages/doenetml-worker/src/components/Function.js
+++ b/packages/doenetml-worker/src/components/Function.js
@@ -16,7 +16,10 @@ import {
     returnRoundingAttributes,
     returnRoundingStateVariableDefinitions,
 } from "../utils/rounding";
-import { returnWrapNonLabelsSugarFunction } from "../utils/label";
+import {
+    returnLabelAttributes,
+    returnWrapNonLabelsSugarFunction,
+} from "../utils/label";
 import {
     find_local_global_maxima,
     find_local_global_minima,
@@ -79,12 +82,8 @@ export default class Function extends InlineComponent {
         // include attributes of graphical components
         // for case when function is adapted into a curve
 
-        attributes.labelIsName = {
-            createComponentOfType: "boolean",
-            createStateVariable: "labelIsName",
-            defaultValue: false,
-            public: true,
-        };
+        Object.assign(attributes, returnLabelAttributes());
+
         attributes.applyStyleToLabel = {
             createComponentOfType: "boolean",
             createStateVariable: "applyStyleToLabel",
diff --git a/packages/doenetml-worker/src/components/MathInput.js b/packages/doenetml-worker/src/components/MathInput.js
index 16f21718f..fc841cbb3 100644
--- a/packages/doenetml-worker/src/components/MathInput.js
+++ b/packages/doenetml-worker/src/components/MathInput.js
@@ -7,6 +7,7 @@ import {
     returnRoundingStateVariableDefinitions,
 } from "../utils/rounding";
 import {
+    returnLabelAttributes,
     returnLabelStateVariableDefinitions,
     returnWrapNonLabelsSugarFunction,
 } from "../utils/label";
@@ -130,12 +131,9 @@ export default class MathInput extends Input {
             public: true,
             forRenderer: true,
         };
-        attributes.labelIsName = {
-            createComponentOfType: "boolean",
-            createStateVariable: "labelIsName",
-            defaultValue: false,
-            public: true,
-        };
+
+        Object.assign(attributes, returnLabelAttributes());
+
         return attributes;
     }
 
diff --git a/packages/doenetml-worker/src/components/Slider.js b/packages/doenetml-worker/src/components/Slider.js
index 0f8ba9ad9..ca410eb9d 100644
--- a/packages/doenetml-worker/src/components/Slider.js
+++ b/packages/doenetml-worker/src/components/Slider.js
@@ -1,7 +1,10 @@
 import { roundForDisplay } from "../utils/math";
 import BaseComponent from "./abstract/BaseComponent";
 import me from "math-expressions";
-import { returnLabelStateVariableDefinitions } from "../utils/label";
+import {
+    returnLabelAttributes,
+    returnLabelStateVariableDefinitions,
+} from "../utils/label";
 import {
     returnRoundingAttributeComponentShadowing,
     returnRoundingAttributes,
@@ -50,12 +53,6 @@ export default class Slider extends BaseComponent {
             createStateVariable: "initialValue",
             defaultValue: null,
         };
-        attributes.labelIsName = {
-            createComponentOfType: "boolean",
-            createStateVariable: "labelIsName",
-            defaultValue: false,
-            public: true,
-        };
         attributes.showControls = {
             createComponentOfType: "boolean",
             createStateVariable: "showControls",
@@ -99,6 +96,8 @@ export default class Slider extends BaseComponent {
             forRenderer: true,
         };
 
+        Object.assign(attributes, returnLabelAttributes());
+
         Object.assign(attributes, returnRoundingAttributes());
 
         attributes.bindValueTo = {
diff --git a/packages/doenetml-worker/src/components/TextInput.js b/packages/doenetml-worker/src/components/TextInput.js
index 8f801059e..0d5d71e35 100644
--- a/packages/doenetml-worker/src/components/TextInput.js
+++ b/packages/doenetml-worker/src/components/TextInput.js
@@ -4,6 +4,7 @@ import {
     returnAnchorStateVariableDefinition,
 } from "../utils/graphical";
 import {
+    returnLabelAttributes,
     returnLabelStateVariableDefinitions,
     returnWrapNonLabelsSugarFunction,
 } from "../utils/label";
@@ -73,12 +74,6 @@ export default class Textinput extends Input {
             forRenderer: true,
             public: true,
         };
-        attributes.labelIsName = {
-            createComponentOfType: "boolean",
-            createStateVariable: "labelIsName",
-            defaultValue: false,
-            public: true,
-        };
         attributes.draggable = {
             createComponentOfType: "boolean",
             createStateVariable: "draggable",
@@ -89,6 +84,8 @@ export default class Textinput extends Input {
 
         Object.assign(attributes, returnAnchorAttributes());
 
+        Object.assign(attributes, returnLabelAttributes());
+
         return attributes;
     }
 
diff --git a/packages/doenetml-worker/src/components/TriggerSet.js b/packages/doenetml-worker/src/components/TriggerSet.js
index cf73ae85c..7e81cd5fb 100644
--- a/packages/doenetml-worker/src/components/TriggerSet.js
+++ b/packages/doenetml-worker/src/components/TriggerSet.js
@@ -3,7 +3,10 @@ import {
     returnAnchorAttributes,
     returnAnchorStateVariableDefinition,
 } from "../utils/graphical";
-import { returnLabelStateVariableDefinitions } from "../utils/label";
+import {
+    returnLabelAttributes,
+    returnLabelStateVariableDefinitions,
+} from "../utils/label";
 import {
     addStandardTriggeringStateVariableDefinitions,
     returnStandardTriggeringAttributes,
@@ -30,13 +33,6 @@ export default class triggerSet extends InlineComponent {
         // attributes.width = {default: 300};
         // attributes.height = {default: 50};
 
-        attributes.labelIsName = {
-            createComponentOfType: "boolean",
-            createStateVariable: "labelIsName",
-            defaultValue: false,
-            public: true,
-        };
-
         attributes.draggable = {
             createComponentOfType: "boolean",
             createStateVariable: "draggable",
@@ -47,6 +43,8 @@ export default class triggerSet extends InlineComponent {
 
         Object.assign(attributes, returnAnchorAttributes());
 
+        Object.assign(attributes, returnLabelAttributes());
+
         let triggerAttributes = returnStandardTriggeringAttributes(
             "triggerActionsIfTriggerNewlyTrue",
         );
diff --git a/packages/doenetml-worker/src/components/UpdateValue.js b/packages/doenetml-worker/src/components/UpdateValue.js
index bfb29b78f..84dee19fd 100644
--- a/packages/doenetml-worker/src/components/UpdateValue.js
+++ b/packages/doenetml-worker/src/components/UpdateValue.js
@@ -3,7 +3,10 @@ import {
     returnAnchorAttributes,
     returnAnchorStateVariableDefinition,
 } from "../utils/graphical";
-import { returnLabelStateVariableDefinitions } from "../utils/label";
+import {
+    returnLabelAttributes,
+    returnLabelStateVariableDefinitions,
+} from "../utils/label";
 import { normalizeMathExpression } from "@doenet/utils";
 import {
     addStandardTriggeringStateVariableDefinitions,
@@ -33,13 +36,6 @@ export default class UpdateValue extends InlineComponent {
         // attributes.width = {default: 300};
         // attributes.height = {default: 50};
 
-        attributes.labelIsName = {
-            createComponentOfType: "boolean",
-            createStateVariable: "labelIsName",
-            defaultValue: false,
-            public: true,
-        };
-
         attributes.type = {
             createPrimitiveOfType: "string",
             createStateVariable: "type",
@@ -98,6 +94,8 @@ export default class UpdateValue extends InlineComponent {
 
         Object.assign(attributes, returnAnchorAttributes());
 
+        Object.assign(attributes, returnLabelAttributes());
+
         let triggerAttributes = returnStandardTriggeringAttributes(
             "updateValueIfTriggerNewlyTrue",
         );
diff --git a/packages/doenetml-worker/src/components/abstract/BaseComponent.js b/packages/doenetml-worker/src/components/abstract/BaseComponent.js
index 1f0e8860c..d057e0408 100644
--- a/packages/doenetml-worker/src/components/abstract/BaseComponent.js
+++ b/packages/doenetml-worker/src/components/abstract/BaseComponent.js
@@ -1202,6 +1202,14 @@ export default class BaseComponent {
             primitiveSourceAttributesToIgnore = [];
         }
 
+        let componentSourceAttributesToIgnore;
+        if (parameters.componentSourceAttributesToIgnore) {
+            componentSourceAttributesToIgnore =
+                parameters.componentSourceAttributesToIgnore;
+        } else {
+            componentSourceAttributesToIgnore = [];
+        }
+
         if (includeDefiningChildren) {
             if (
                 this.constructor.serializeReplacementsForChildren &&
@@ -1246,8 +1254,15 @@ export default class BaseComponent {
         for (let attrName in this.attributes) {
             let attribute = this.attributes[attrName];
             if (attribute.component) {
-                // only copy attribute components if copy all
-                if (parameters.copyAll) {
+                // only copy attribute components if copy all and not set to be ignored
+                // Note that, unlike for the primitive case, below,
+                // attributeToIgnore supersedes copyAll.
+                // As of Nov 2024, the only componentSourceAttributesToIgnore
+                // is labelIsName when copying without link.
+                if (
+                    parameters.copyAll &&
+                    !componentSourceAttributesToIgnore.includes(attrName)
+                ) {
                     serializedComponent.attributes[attrName] = {
                         component: await attribute.component.serialize(
                             parametersForChildren,
diff --git a/packages/doenetml-worker/src/components/abstract/GraphicalComponent.js b/packages/doenetml-worker/src/components/abstract/GraphicalComponent.js
index 67771552a..b88229d81 100644
--- a/packages/doenetml-worker/src/components/abstract/GraphicalComponent.js
+++ b/packages/doenetml-worker/src/components/abstract/GraphicalComponent.js
@@ -1,18 +1,18 @@
 import BaseComponent from "./BaseComponent";
 import { returnSelectedStyleStateVariableDefinition } from "@doenet/utils";
-import { returnLabelStateVariableDefinitions } from "../../utils/label";
+import {
+    returnLabelAttributes,
+    returnLabelStateVariableDefinitions,
+} from "../../utils/label";
 
 export default class GraphicalComponent extends BaseComponent {
     static componentType = "_graphical";
 
     static createAttributesObject() {
         let attributes = super.createAttributesObject();
-        attributes.labelIsName = {
-            createComponentOfType: "boolean",
-            createStateVariable: "labelIsName",
-            defaultValue: false,
-            public: true,
-        };
+
+        Object.assign(attributes, returnLabelAttributes());
+
         attributes.applyStyleToLabel = {
             createComponentOfType: "boolean",
             createStateVariable: "applyStyleToLabel",
diff --git a/packages/doenetml-worker/src/test/graphical/labels.test.ts b/packages/doenetml-worker/src/test/graphical/labels.test.ts
new file mode 100644
index 000000000..904dfce85
--- /dev/null
+++ b/packages/doenetml-worker/src/test/graphical/labels.test.ts
@@ -0,0 +1,893 @@
+import { describe, expect, it, vi } from "vitest";
+import { createTestCore, returnAllStateVariables } from "../utils/test-core";
+import { updateTextInputValue } from "../utils/actions";
+import Core from "../../Core";
+
+const Mock = vi.fn();
+vi.stubGlobal("postMessage", Mock);
+vi.mock("hyperformula");
+
+describe("Label tests", async () => {
+    async function test_labelIsName_preserved_shadowed_or_no_link(core: Core) {
+        const stateVariables = await returnAllStateVariables(core);
+
+        expect(stateVariables["/Plabel"].stateValues.value).eq("P");
+        expect(stateVariables["/Qlabel"].stateValues.value).eq("Q");
+        expect(stateVariables["/Rlabel"].stateValues.value).eq("R");
+        expect(stateVariables["/Slabel"].stateValues.value).eq("S");
+        expect(stateVariables["/g2Plabel"].stateValues.value).eq("P");
+        expect(stateVariables["/g2Qlabel"].stateValues.value).eq("Q");
+        expect(stateVariables["/g2Rlabel"].stateValues.value).eq("R");
+        expect(stateVariables["/g2Slabel"].stateValues.value).eq("S");
+        expect(stateVariables["/Q3label"].stateValues.value).eq("Q");
+        expect(stateVariables["/S3label"].stateValues.value).eq("S");
+        expect(stateVariables["/Q4label"].stateValues.value).eq("Q");
+        expect(stateVariables["/S4label"].stateValues.value).eq("S");
+        expect(stateVariables["/g5Plabel"].stateValues.value).eq("P");
+        expect(stateVariables["/g5Qlabel"].stateValues.value).eq("Q");
+        expect(stateVariables["/g5Rlabel"].stateValues.value).eq("R");
+        expect(stateVariables["/g5Slabel"].stateValues.value).eq("S");
+        expect(stateVariables["/g5Plabel"].stateValues.value).eq("P");
+        expect(stateVariables["/g6Qlabel"].stateValues.value).eq("Q");
+        expect(stateVariables["/g6Slabel"].stateValues.value).eq("S");
+        expect(stateVariables["/g7Qlabel"].stateValues.value).eq("Q");
+        expect(stateVariables["/g7Slabel"].stateValues.value).eq("S");
+
+        let P2Name = stateVariables["/g2"].activeChildren[0].componentName;
+        let Q2Name = stateVariables["/g2"].activeChildren[1].componentName;
+        let R2Name = stateVariables["/g2"].activeChildren[2].componentName;
+        let S2Name = stateVariables["/g2"].activeChildren[3].componentName;
+        let P3Name = stateVariables["/g3"].activeChildren[0].componentName;
+        let Q3Name = stateVariables["/g3"].activeChildren[1].componentName;
+        let R3Name = stateVariables["/g3"].activeChildren[2].componentName;
+        let S3Name = stateVariables["/g3"].activeChildren[3].componentName;
+        let P4Name = stateVariables["/g4"].activeChildren[0].componentName;
+        let Q4Name = stateVariables["/g4"].activeChildren[1].componentName;
+        let R4Name = stateVariables["/g4"].activeChildren[2].componentName;
+        let S4Name = stateVariables["/g4"].activeChildren[3].componentName;
+        let P5Name = stateVariables["/g5"].activeChildren[0].componentName;
+        let Q5Name = stateVariables["/g5"].activeChildren[1].componentName;
+        let R5Name = stateVariables["/g5"].activeChildren[2].componentName;
+        let S5Name = stateVariables["/g5"].activeChildren[3].componentName;
+        let P6Name = stateVariables["/g6"].activeChildren[0].componentName;
+        let Q6Name = stateVariables["/g6"].activeChildren[1].componentName;
+        let R6Name = stateVariables["/g6"].activeChildren[2].componentName;
+        let S6Name = stateVariables["/g6"].activeChildren[3].componentName;
+        let P7Name = stateVariables["/g7"].activeChildren[0].componentName;
+        let Q7Name = stateVariables["/g7"].activeChildren[1].componentName;
+        let R7Name = stateVariables["/g7"].activeChildren[2].componentName;
+        let S7Name = stateVariables["/g7"].activeChildren[3].componentName;
+
+        expect(stateVariables["/P"].stateValues.label).eq("P");
+        expect(stateVariables["/P"].stateValues.labelForGraph).eq("P");
+        expect(stateVariables["/Q"].stateValues.label).eq("Q");
+        expect(stateVariables["/Q"].stateValues.labelForGraph).eq("Q");
+        expect(stateVariables["/R"].stateValues.label).eq("R");
+        expect(stateVariables["/R"].stateValues.labelForGraph).eq("R");
+        expect(stateVariables["/S"].stateValues.label).eq("S");
+        expect(stateVariables["/S"].stateValues.labelForGraph).eq("S");
+        expect(stateVariables[P2Name].stateValues.label).eq("P");
+        expect(stateVariables[P2Name].stateValues.labelForGraph).eq("P");
+        expect(stateVariables[Q2Name].stateValues.label).eq(`Q`);
+        expect(stateVariables[Q2Name].stateValues.labelForGraph).eq(`Q`);
+        expect(stateVariables[R2Name].stateValues.label).eq(`R`);
+        expect(stateVariables[R2Name].stateValues.labelForGraph).eq(`R`);
+        expect(stateVariables[S2Name].stateValues.label).eq(`S`);
+        expect(stateVariables[S2Name].stateValues.labelForGraph).eq(`S`);
+        expect(stateVariables["/Q3"].stateValues.label).eq(`Q`);
+        expect(stateVariables["/Q3"].stateValues.labelForGraph).eq(`Q`);
+        expect(stateVariables["/S3"].stateValues.label).eq(`S`);
+        expect(stateVariables["/S3"].stateValues.labelForGraph).eq(`S`);
+        expect(stateVariables[P3Name].stateValues.label).eq("P");
+        expect(stateVariables[P3Name].stateValues.labelForGraph).eq("P");
+        expect(stateVariables[Q3Name].stateValues.label).eq(`Q`);
+        expect(stateVariables[Q3Name].stateValues.labelForGraph).eq(`Q`);
+        expect(stateVariables[R3Name].stateValues.label).eq(`R`);
+        expect(stateVariables[R3Name].stateValues.labelForGraph).eq(`R`);
+        expect(stateVariables[S3Name].stateValues.label).eq(`S`);
+        expect(stateVariables[S3Name].stateValues.labelForGraph).eq(`S`);
+        expect(stateVariables["/Q4"].stateValues.label).eq(`Q`);
+        expect(stateVariables["/Q4"].stateValues.labelForGraph).eq(`Q`);
+        expect(stateVariables["/S4"].stateValues.label).eq(`S`);
+        expect(stateVariables["/S4"].stateValues.labelForGraph).eq(`S`);
+        expect(stateVariables[P4Name].stateValues.label).eq("P");
+        expect(stateVariables[P4Name].stateValues.labelForGraph).eq("P");
+        expect(stateVariables[Q4Name].stateValues.label).eq(`Q`);
+        expect(stateVariables[Q4Name].stateValues.labelForGraph).eq(`Q`);
+        expect(stateVariables[R4Name].stateValues.label).eq(`R`);
+        expect(stateVariables[R4Name].stateValues.labelForGraph).eq(`R`);
+        expect(stateVariables[S4Name].stateValues.label).eq(`S`);
+        expect(stateVariables[S4Name].stateValues.labelForGraph).eq(`S`);
+        expect(stateVariables[P5Name].stateValues.label).eq("P");
+        expect(stateVariables[P5Name].stateValues.labelForGraph).eq("P");
+        expect(stateVariables[Q5Name].stateValues.label).eq(`Q`);
+        expect(stateVariables[Q5Name].stateValues.labelForGraph).eq(`Q`);
+        expect(stateVariables[R5Name].stateValues.label).eq(`R`);
+        expect(stateVariables[R5Name].stateValues.labelForGraph).eq(`R`);
+        expect(stateVariables[S5Name].stateValues.label).eq(`S`);
+        expect(stateVariables[S5Name].stateValues.labelForGraph).eq(`S`);
+        expect(stateVariables[P6Name].stateValues.label).eq("P");
+        expect(stateVariables[P6Name].stateValues.labelForGraph).eq("P");
+        expect(stateVariables[Q6Name].stateValues.label).eq(`Q`);
+        expect(stateVariables[Q6Name].stateValues.labelForGraph).eq(`Q`);
+        expect(stateVariables[R6Name].stateValues.label).eq(`R`);
+        expect(stateVariables[R6Name].stateValues.labelForGraph).eq(`R`);
+        expect(stateVariables[S6Name].stateValues.label).eq(`S`);
+        expect(stateVariables[S6Name].stateValues.labelForGraph).eq(`S`);
+        expect(stateVariables[P7Name].stateValues.label).eq("P");
+        expect(stateVariables[P7Name].stateValues.labelForGraph).eq("P");
+        expect(stateVariables[Q7Name].stateValues.label).eq(`Q`);
+        expect(stateVariables[Q7Name].stateValues.labelForGraph).eq(`Q`);
+        expect(stateVariables[R7Name].stateValues.label).eq(`R`);
+        expect(stateVariables[R7Name].stateValues.labelForGraph).eq(`R`);
+        expect(stateVariables[S7Name].stateValues.label).eq(`S`);
+        expect(stateVariables[S7Name].stateValues.labelForGraph).eq(`S`);
+    }
+
+    it("labels from labelIsName are preserved when shadowed", async () => {
+        let core = await createTestCore({
+            doenetML: `
+  <graph name="g">
+    <point name="P" labelIsName>(1,2)</point>
+    <point name="Q" labelIsName>(3,4)</point>
+    <point name="R" labelIsName>(5,6)</point>
+    <point name="S" labelIsName>(7,8)</point>
+  </graph>
+
+  <graph name="g2" copySource="g" newNamespace />
+
+  <graph name="g3">
+     $P
+     $Q{name="Q3"}
+     <point copySource="R" />
+     <point name="S3" copySource="S" />
+  </graph>
+
+  <graph name="g4">
+     $P{labelIsName="false"}
+     $Q{name="Q4" labelIsName="false"}
+     <point copySource="R" labelIsName="false" />
+     <point name="S4" copySource="S" labelIsName="false" />
+  </graph>
+
+  <graph copySource="g2" name="g5" newNamespace />
+  <graph copySource="g3" name="g6" newNamespace />
+  <graph copySource="g4" name="g7" newNamespace />
+
+  <p>P label: <label copySource="P.label" name="Plabel" /></p>
+  <p>Q label: <label copySource="Q.label" name="Qlabel" /></p>
+  <p>R label: <label copySource="R.label" name="Rlabel" /></p>
+  <p>S label: <label copySource="S.label" name="Slabel" /></p>
+  <p>g2/P label: <label copySource="g2/P.label" name="g2Plabel" /></p>
+  <p>g2/Q label: <label copySource="g2/Q.label" name="g2Qlabel" /></p>
+  <p>g2/R label: <label copySource="g2/R.label" name="g2Rlabel" /></p>
+  <p>g2/S label: <label copySource="g2/S.label" name="g2Slabel" /></p>
+  <p>Q3 label: <label copySource="Q3.label" name="Q3label" /></p>
+  <p>S3 label: <label copySource="S3.label" name="S3label" /></p>
+  <p>Q4 label: <label copySource="Q4.label" name="Q4label" /></p>
+  <p>S4 label: <label copySource="S4.label" name="S4label" /></p>
+  <p>g5/P label: <label copySource="g5/P.label" name="g5Plabel" /></p>
+  <p>g5/Q label: <label copySource="g5/Q.label" name="g5Qlabel" /></p>
+  <p>g5/R label: <label copySource="g5/R.label" name="g5Rlabel" /></p>
+  <p>g5/S label: <label copySource="g5/S.label" name="g5Slabel" /></p>
+  <p>g6/Q3 label: <label copySource="g6/Q3.label" name="g6Qlabel" /></p>
+  <p>g6/S3 label: <label copySource="g6/S3.label" name="g6Slabel" /></p>
+  <p>g7/Q4 label: <label copySource="g7/Q4.label" name="g7Qlabel" /></p>
+  <p>g7/S4 label: <label copySource="g7/S4.label" name="g7Slabel" /></p>
+
+    `,
+        });
+
+        await test_labelIsName_preserved_shadowed_or_no_link(core);
+    });
+
+    it("labels from labelIsName are preserved when copy with link=false", async () => {
+        let core = await createTestCore({
+            doenetML: `
+<graph name="g">
+  <point name="P" labelIsName>(1,2)</point>
+  <point name="Q" labelIsName>(3,4)</point>
+  <point name="R" labelIsName>(5,6)</point>
+  <point name="S" labelIsName>(7,8)</point>
+</graph>
+
+<graph name="g2" copySource="g" newNamespace link="false" />
+
+<graph name="g3">
+  $P{link="false"}
+  $Q{name="Q3" link="false"}
+  <point copySource="R" link="false" />
+  <point name="S3" copySource="S" link="false" />
+</graph>
+
+<graph name="g4">
+  $P{labelIsName="false" link="false"}
+  $Q{name="Q4" labelIsName="false" link="false"}
+  <point copySource="R" labelIsName="false" link="false" />
+  <point name="S4" copySource="S" labelIsName="false" link="false" />
+</graph>
+
+<graph copySource="g2" name="g5" newNamespace link="false" />
+<graph copySource="g3" name="g6" newNamespace link="false" />
+<graph copySource="g4" name="g7" newNamespace link="false" />
+
+<p>P label: <label copySource="P.label" name="Plabel" /></p>
+<p>Q label: <label copySource="Q.label" name="Qlabel" /></p>
+<p>R label: <label copySource="R.label" name="Rlabel" /></p>
+<p>S label: <label copySource="S.label" name="Slabel" /></p>
+<p>g2/P label: <label copySource="g2/P.label" name="g2Plabel" /></p>
+<p>g2/Q label: <label copySource="g2/Q.label" name="g2Qlabel" /></p>
+<p>g2/R label: <label copySource="g2/R.label" name="g2Rlabel" /></p>
+<p>g2/S label: <label copySource="g2/S.label" name="g2Slabel" /></p>
+<p>Q3 label: <label copySource="Q3.label" name="Q3label" /></p>
+<p>S3 label: <label copySource="S3.label" name="S3label" /></p>
+<p>Q4 label: <label copySource="Q4.label" name="Q4label" /></p>
+<p>S4 label: <label copySource="S4.label" name="S4label" /></p>
+<p>g5/P label: <label copySource="g5/P.label" name="g5Plabel" /></p>
+<p>g5/Q label: <label copySource="g5/Q.label" name="g5Qlabel" /></p>
+<p>g5/R label: <label copySource="g5/R.label" name="g5Rlabel" /></p>
+<p>g5/S label: <label copySource="g5/S.label" name="g5Slabel" /></p>
+<p>g6/Q3 label: <label copySource="g6/Q3.label" name="g6Qlabel" /></p>
+<p>g6/S3 label: <label copySource="g6/S3.label" name="g6Slabel" /></p>
+<p>g7/Q4 label: <label copySource="g7/Q4.label" name="g7Qlabel" /></p>
+<p>g7/S4 label: <label copySource="g7/S4.label" name="g7Slabel" /></p>
+
+    `,
+        });
+
+        await test_labelIsName_preserved_shadowed_or_no_link(core);
+    });
+
+    it("labelIsName in map", async () => {
+        let core = await createTestCore({
+            doenetML: `
+  <graph name="g1" newNamespace>
+    <map>
+      <template><point name="P" labelIsName>($v,1)</point></template>
+      <sources alias="v"><sequence from="-2" to="2" /></sources>
+    </map>
+  </graph>
+
+  <graph name="g2" newNamespace>
+    <map>
+      <template newNamespace><vector name="P" labelIsName>($v,1)</vector></template>
+      <sources alias="v"><sequence from="-2" to="2" /></sources>
+    </map>
+  </graph>
+
+  <graph name="g3" newNamespace>
+    <map assignNames="(A) (B) (C)">
+      <template><circle name="P" labelIsName center="($v,1)" /"></template>
+      <sources alias="v"><sequence from="-2" to="2" /></sources>
+    </map>
+  </graph>
+
+  <graph name="g4" newNamespace>
+    <map assignNames="(A) (B) (C)">
+      <template newNamespace><line name="P" labelIsName through="($v,1)" /></template>
+      <sources alias="v"><sequence from="-2" to="2" /></sources>
+    </map>
+  </graph>
+
+  <graph name="g5" newNamespace>
+    <map assignNames="A B C">
+      <template><triangle name="P" labelIsName vertex="($v,1)" /></template>
+      <sources alias="v"><sequence from="-2" to="2" /></sources>
+    </map>
+  </graph>
+
+  <graph name="g6" newNamespace>
+    <map assignNames="A B C">
+      <template newNamespace><lineSegment name="P" labelIsName endPoint="($v,1)" /></template>
+      <sources alias="v"><sequence from="-2" to="2" /></sources>
+    </map>
+  </graph>
+
+
+  $g1{name="g7"}
+  $g2{name="g8"}
+  $g3{name="g9"}
+  $g4{name="g10"}
+  $g5{name="g11"}
+  $g6{name="g12"}
+    `,
+        });
+
+        let stateVariables = await returnAllStateVariables(core);
+
+        let g1ChildNames = stateVariables["/g1"].activeChildren.map(
+            (x) => x.componentName,
+        );
+        let g2ChildNames = stateVariables["/g2"].activeChildren.map(
+            (x) => x.componentName,
+        );
+        let g3ChildNames = stateVariables["/g3"].activeChildren.map(
+            (x) => x.componentName,
+        );
+        let g4ChildNames = stateVariables["/g4"].activeChildren.map(
+            (x) => x.componentName,
+        );
+        let g5ChildNames = stateVariables["/g5"].activeChildren.map(
+            (x) => x.componentName,
+        );
+        let g6ChildNames = stateVariables["/g6"].activeChildren.map(
+            (x) => x.componentName,
+        );
+        let g7ChildNames = stateVariables["/g7"].activeChildren.map(
+            (x) => x.componentName,
+        );
+        let g8ChildNames = stateVariables["/g8"].activeChildren.map(
+            (x) => x.componentName,
+        );
+        let g9ChildNames = stateVariables["/g9"].activeChildren.map(
+            (x) => x.componentName,
+        );
+        let g10ChildNames = stateVariables["/g10"].activeChildren.map(
+            (x) => x.componentName,
+        );
+        let g11ChildNames = stateVariables["/g11"].activeChildren.map(
+            (x) => x.componentName,
+        );
+        let g12ChildNames = stateVariables["/g12"].activeChildren.map(
+            (x) => x.componentName,
+        );
+
+        let g1ChildLabels = Array(5).fill("");
+        let g2ChildLabels = Array(5).fill("P");
+        let g3ChildLabels = ["A", "B", "C", "", ""];
+        let g4ChildLabels = ["A", "B", "C", "P", "P"];
+        let g5ChildLabels = Array(5).fill("");
+        let g6ChildLabels = Array(5).fill("P");
+
+        for (let [ind, name] of g1ChildNames.entries()) {
+            expect(stateVariables[name].stateValues.label).eq(
+                g1ChildLabels[ind],
+            );
+        }
+        for (let [ind, name] of g2ChildNames.entries()) {
+            expect(stateVariables[name].stateValues.label).eq(
+                g2ChildLabels[ind],
+            );
+        }
+        for (let [ind, name] of g3ChildNames.entries()) {
+            expect(stateVariables[name].stateValues.label).eq(
+                g3ChildLabels[ind],
+            );
+        }
+        for (let [ind, name] of g4ChildNames.entries()) {
+            expect(stateVariables[name].stateValues.label).eq(
+                g4ChildLabels[ind],
+            );
+        }
+        for (let [ind, name] of g5ChildNames.entries()) {
+            expect(stateVariables[name].stateValues.label).eq(
+                g5ChildLabels[ind],
+            );
+        }
+        for (let [ind, name] of g6ChildNames.entries()) {
+            expect(stateVariables[name].stateValues.label).eq(
+                g6ChildLabels[ind],
+            );
+        }
+
+        for (let [ind, name] of g7ChildNames.entries()) {
+            expect(stateVariables[name].stateValues.label).eq(
+                g1ChildLabels[ind],
+            );
+        }
+        for (let [ind, name] of g8ChildNames.entries()) {
+            expect(stateVariables[name].stateValues.label).eq(
+                g2ChildLabels[ind],
+            );
+        }
+        for (let [ind, name] of g9ChildNames.entries()) {
+            expect(stateVariables[name].stateValues.label).eq(
+                g3ChildLabels[ind],
+            );
+        }
+        for (let [ind, name] of g10ChildNames.entries()) {
+            expect(stateVariables[name].stateValues.label).eq(
+                g4ChildLabels[ind],
+            );
+        }
+        for (let [ind, name] of g11ChildNames.entries()) {
+            expect(stateVariables[name].stateValues.label).eq(
+                g5ChildLabels[ind],
+            );
+        }
+        for (let [ind, name] of g12ChildNames.entries()) {
+            expect(stateVariables[name].stateValues.label).eq(
+                g6ChildLabels[ind],
+            );
+        }
+    });
+
+    it("labelIsName in newNamespace", async () => {
+        let core = await createTestCore({
+            doenetML: `
+  <graph name="g" newNamespace>
+    <point name="P" labelIsName>(5,6)</point>
+  </graph>
+    `,
+        });
+
+        let stateVariables = await returnAllStateVariables(core);
+        expect(stateVariables["/g/P"].stateValues.label).eq("P");
+    });
+
+    it("labelIsName converts case", async () => {
+        let core = await createTestCore({
+            doenetML: `
+  <graph>
+    <point name="the_first_point" labelIsName>(5,6)</point>
+    <point name="the-second-point" labelIsName>(1,3)</point>
+    <point name="theThirdPoint" labelIsName>(-2,1)</point>
+    <point name="TheFourthPoint" labelIsName>(7,-5)</point>
+    <point name="the-FIFTH_Point" labelIsName>(-6,-8)</point>
+    <point name="the_SiXiTH-Point" labelIsName>(9,0)</point>
+  </graph>
+    `,
+        });
+
+        let stateVariables = await returnAllStateVariables(core);
+        expect(stateVariables["/the_first_point"].stateValues.label).eq(
+            "the first point",
+        );
+        expect(stateVariables["/the-second-point"].stateValues.label).eq(
+            "the second point",
+        );
+        expect(stateVariables["/theThirdPoint"].stateValues.label).eq(
+            "the third point",
+        );
+        expect(stateVariables["/TheFourthPoint"].stateValues.label).eq(
+            "The Fourth Point",
+        );
+        expect(stateVariables["/the-FIFTH_Point"].stateValues.label).eq(
+            "the FIFTH Point",
+        );
+        expect(stateVariables["/the_SiXiTH-Point"].stateValues.label).eq(
+            "the SiXiTH Point",
+        );
+    });
+
+    it("labelIsName and copies", async () => {
+        // Note: we add groups just so that we can reference the children
+        // inside the DoenetML
+        let core = await createTestCore({
+            doenetML: `
+  <graph>
+    <point name="A" labelIsName />
+  </graph>
+  <graph>
+    <point copySource="A" name="B" />
+  </graph>
+  <graph>
+    $A{name="C"}
+  </graph>
+  <graph>
+    <point copySource="A" name="D" labelIsName/>
+  </graph>
+  <graph>
+    $A{name="E" labelIsName}
+  </graph>
+  <graph name="g6">
+    <group name="grp1"><point copySource="A" labelIsName/></group>
+  </graph>
+  <graph name="g7">
+    <group name="grp2">$A{labelIsName}</group>
+  </graph>
+
+  <p><text copySource="A" copyProp="label" name="lA" /></p>
+  <p><label copySource="B" copyProp="label" name="lB" /></p>
+  <p><text copySource="C" copyProp="label" name="lC" /></p>
+  <p><label copySource="D" copyProp="label" name="lD" /></p>
+  <p><text copySource="E" copyProp="label" name="lE" /></p>
+  <p><label copySource="grp1[1].label" name="lp6" /></p>
+  <p><label copySource="grp2[1].label" name="lp7" /></p>
+
+  <p><textInput bindValueTo="$A.label" name="tiA" /></p>
+  <p><textInput bindValueTo="$B.label" name="tiB" /></p>
+  <p><textInput bindValueTo="$C.label" name="tiC" /></p>
+  <p><textInput bindValueTo="$D.label" name="tiD" /></p>
+  <p><textInput bindValueTo="$E.label" name="tiE" /></p>
+  <p><textInput bindValueTo="$grp1[1].label" name="tip6" /></p>
+  <p><textInput bindValueTo="$grp2[1].label" name="tip7" /></p>
+    `,
+        });
+
+        async function check_items({ lA, lD, lE, l6, l7 }) {
+            const stateVariables = await returnAllStateVariables(core);
+            const p6Name =
+                stateVariables["/g6"].activeChildren[0].componentName;
+            const p7Name =
+                stateVariables["/g7"].activeChildren[0].componentName;
+
+            expect(stateVariables["/lA"].stateValues.value).eq(lA);
+            expect(stateVariables["/lB"].stateValues.value).eq(lA);
+            expect(stateVariables["/lC"].stateValues.value).eq(lA);
+            expect(stateVariables["/lD"].stateValues.value).eq(lD);
+            expect(stateVariables["/lE"].stateValues.value).eq(lE);
+            expect(stateVariables["/lp6"].stateValues.value).eq(l6);
+            expect(stateVariables["/lp7"].stateValues.value).eq(l7);
+
+            expect(stateVariables["/A"].stateValues.label).eq(lA);
+            expect(stateVariables["/A"].stateValues.labelForGraph).eq(lA);
+            expect(stateVariables["/B"].stateValues.label).eq(lA);
+            expect(stateVariables["/B"].stateValues.labelForGraph).eq(lA);
+            expect(stateVariables["/C"].stateValues.label).eq(lA);
+            expect(stateVariables["/C"].stateValues.labelForGraph).eq(lA);
+            expect(stateVariables["/D"].stateValues.label).eq(lD);
+            expect(stateVariables["/D"].stateValues.labelForGraph).eq(lD);
+            expect(stateVariables["/E"].stateValues.label).eq(lE);
+            expect(stateVariables["/E"].stateValues.labelForGraph).eq(lE);
+            expect(stateVariables[p6Name].stateValues.label).eq(l6);
+            expect(stateVariables[p6Name].stateValues.labelForGraph).eq(l6);
+            expect(stateVariables[p7Name].stateValues.label).eq(l7);
+            expect(stateVariables[p7Name].stateValues.labelForGraph).eq(l7);
+        }
+
+        let lA = "A",
+            lD = "D",
+            lE = "E",
+            l6 = "A",
+            l7 = "A";
+        await check_items({ lA, lD, lE, l6, l7 });
+
+        lA = "F";
+        await updateTextInputValue({ text: lA, name: "/tiA", core });
+        await check_items({ lA, lD, lE, l6, l7 });
+
+        lA = "G";
+        await updateTextInputValue({ name: "/tiB", text: lA, core });
+        await check_items({ lA, lD, lE, l6, l7 });
+
+        lA = "H";
+        await updateTextInputValue({ name: "/tiC", text: lA, core });
+        await check_items({ lA, lD, lE, l6, l7 });
+
+        lD = "I";
+        await updateTextInputValue({ name: "/tiD", text: lD, core });
+        await check_items({ lA, lD, lE, l6, l7 });
+
+        lE = "J";
+        await updateTextInputValue({ name: "/tiE", text: lE, core });
+        await check_items({ lA, lD, lE, l6, l7 });
+
+        l6 = "K";
+        await updateTextInputValue({ name: "/tip6", text: l6, core });
+        await check_items({ lA, lD, lE, l6, l7 });
+
+        l7 = "L";
+        await updateTextInputValue({ name: "/tip7", text: l7, core });
+        await check_items({ lA, lD, lE, l6, l7 });
+    });
+
+    it("copy and add labelIsName", async () => {
+        let core = await createTestCore({
+            doenetML: `
+  <graph>
+    <point name="A" />
+  </graph>
+  <graph>
+    <point copySource="A" name="B" labelIsName />
+  </graph>
+  <graph>
+    $A{name="C" labelIsName}
+  </graph>
+  <graph name="g4">
+    <group name="grp1"><point copySource="A" labelIsName/></group>
+  </graph>
+  <graph name="g5">
+    <group name="grp2">$A{labelIsName}</group>
+  </graph>
+
+  <p><text copySource="A" copyProp="label" name="lA" /></p>
+  <p><label copySource="B" copyProp="label" name="lB" /></p>
+  <p><text copySource="C" copyProp="label" name="lC" /></p>
+  <p><label copySource="grp1[1].label" name="lp4" /></p>
+  <p><label copySource="grp2[1].label" name="lp5" /></p>
+
+  <p><textInput bindValueTo="$A.label" name="tiA" /></p>
+  <p><textInput bindValueTo="$B.label" name="tiB" /></p>
+  <p><textInput bindValueTo="$C.label" name="tiC" /></p>
+  <p><textInput bindValueTo="$grp1[1].label" name="tip4" /></p>
+  <p><textInput bindValueTo="$grp2[1].label" name="tip5" /></p>
+`,
+        });
+
+        async function check_items({ lA, lB, lC, l4, l5 }) {
+            const stateVariables = await returnAllStateVariables(core);
+            const p4Name =
+                stateVariables["/g4"].activeChildren[0].componentName;
+            const p5Name =
+                stateVariables["/g5"].activeChildren[0].componentName;
+
+            expect(stateVariables["/lA"].stateValues.value).eq(lA);
+            expect(stateVariables["/lB"].stateValues.value).eq(lB);
+            expect(stateVariables["/lC"].stateValues.value).eq(lC);
+            expect(stateVariables["/lp4"].stateValues.value).eq(l4);
+            expect(stateVariables["/lp5"].stateValues.value).eq(l5);
+
+            expect(stateVariables["/A"].stateValues.label).eq(lA);
+            expect(stateVariables["/A"].stateValues.labelForGraph).eq(lA);
+            expect(stateVariables["/B"].stateValues.label).eq(lB);
+            expect(stateVariables["/B"].stateValues.labelForGraph).eq(lB);
+            expect(stateVariables["/C"].stateValues.label).eq(lC);
+            expect(stateVariables["/C"].stateValues.labelForGraph).eq(lC);
+            expect(stateVariables[p4Name].stateValues.label).eq(l4);
+            expect(stateVariables[p4Name].stateValues.labelForGraph).eq(l4);
+            expect(stateVariables[p5Name].stateValues.label).eq(l5);
+            expect(stateVariables[p5Name].stateValues.labelForGraph).eq(l5);
+        }
+
+        let lA = "",
+            lB = "B",
+            lC = "C",
+            l4 = "A",
+            l5 = "A";
+        await check_items({ lA, lB, lC, l4, l5 });
+
+        lA = "F";
+        await updateTextInputValue({ text: lA, name: "/tiA", core });
+        await check_items({ lA, lB, lC, l4, l5 });
+
+        lB = "G";
+        await updateTextInputValue({ name: "/tiB", text: lB, core });
+        await check_items({ lA, lB, lC, l4, l5 });
+
+        lC = "H";
+        await updateTextInputValue({ name: "/tiC", text: lC, core });
+        await check_items({ lA, lB, lC, l4, l5 });
+
+        l4 = "I";
+        await updateTextInputValue({ name: "/tip4", text: l4, core });
+        await check_items({ lA, lB, lC, l4, l5 });
+
+        l5 = "J";
+        await updateTextInputValue({ name: "/tip5", text: l5, core });
+        await check_items({ lA, lB, lC, l4, l5 });
+    });
+
+    async function test_label_labelIsName_copies(
+        doenetMLForA: string,
+        useLabelCopies = false,
+    ) {
+        const labelD = useLabelCopies
+            ? `<label copySource="Dl"/>`
+            : `<label>D</label>`;
+        const labelG = useLabelCopies
+            ? `<label copySource="Gl"/>`
+            : `<label>G</label>`;
+        const labelJ = useLabelCopies
+            ? `<label copySource="Jl"/>`
+            : `<label>J</label>`;
+
+        let labelDefinitions = "";
+        if (useLabelCopies) {
+            labelDefinitions = `
+      <label name="Al0">A</label>
+      <label name="Al" copySource="Al0" />
+      <label name="Dl">D</label>
+      <label name="Gl0">G</label>
+      <label name="Gl" copySource="Gl0" />
+      <label name="Jl0">J</label>
+      <label name="Jl1" copySource="Jl0" />
+      <label name="Jl" copySource="Jl1" />
+            `;
+        }
+
+        let core = await createTestCore({
+            doenetML: `
+    <graph>
+
+        ${doenetMLForA}
+        <point copySource="A" name="B" x="1" />
+        <point copySource="A" labelIsName name="C" x="2" />
+        <point copySource="A" name="D" x="3">${labelD}</point>
+
+        <point copySource="B" name="E" x="1" y="1" />
+        <point copySource="B" labelIsName name="F" x="2" y="1" />
+        <point copySource="B" name="G" x="3" y="1">${labelG}</point>
+
+        <point copySource="C" name="H" x="1" y="2" />
+        <point copySource="C" labelIsName name="I" x="2" y="2" />
+        <point copySource="C" name="J" x="3" y="2">${labelJ}</point>
+
+        <point copySource="D" name="K" x="1" y="3" />
+        <point copySource="D" labelIsName name="L" x="2" y="3" />
+        <point copySource="D" name="M" x="3" y="3"><label>M</label></point>
+
+    </graph>
+
+    ${labelDefinitions}
+
+    <p><text copySource="A.label" name="lA" /></p>
+    <p><text copySource="B.label" name="lB" /></p>
+    <p><text copySource="C.label" name="lC" /></p>
+    <p><text copySource="D.label" name="lD" /></p>
+    <p><text copySource="E.label" name="lE" /></p>
+    <p><text copySource="F.label" name="lF" /></p>
+    <p><text copySource="G.label" name="lG" /></p>
+    <p><text copySource="H.label" name="lH" /></p>
+    <p><text copySource="I.label" name="lI" /></p>
+    <p><text copySource="J.label" name="lJ" /></p>
+    <p><text copySource="K.label" name="lK" /></p>
+    <p><text copySource="L.label" name="lL" /></p>
+    <p><text copySource="M.label" name="lM" /></p>
+
+    <p>Change label of A: <textInput bindValueTo="$A.label" name="tiA" /></p>
+    <p>Change label of B: <textInput bindValueTo="$B.label" name="tiB" /></p>
+    <p>Change label of C: <textInput bindValueTo="$C.label" name="tiC" /></p>
+    <p>Change label of D: <textInput bindValueTo="$D.label" name="tiD" /></p>
+    <p>Change label of E: <textInput bindValueTo="$E.label" name="tiE" /></p>
+    <p>Change label of F: <textInput bindValueTo="$F.label" name="tiF" /></p>
+    <p>Change label of G: <textInput bindValueTo="$G.label" name="tiG" /></p>
+    <p>Change label of H: <textInput bindValueTo="$H.label" name="tiH" /></p>
+    <p>Change label of I: <textInput bindValueTo="$I.label" name="tiI" /></p>
+    <p>Change label of J: <textInput bindValueTo="$J.label" name="tiJ" /></p>
+    <p>Change label of K: <textInput bindValueTo="$K.label" name="tiK" /></p>
+    <p>Change label of L: <textInput bindValueTo="$L.label" name="tiL" /></p>
+    <p>Change label of M: <textInput bindValueTo="$M.label" name="tiM" /></p>
+
+    `,
+        });
+
+        async function check_items({ lA, lC, lD, lF, lG, lI, lJ, lL, lM }) {
+            const stateVariables = await returnAllStateVariables(core);
+            expect(stateVariables["/lA"].stateValues.value).eq(lA);
+            expect(stateVariables["/lB"].stateValues.value).eq(lA);
+            expect(stateVariables["/lC"].stateValues.value).eq(lC);
+            expect(stateVariables["/lD"].stateValues.value).eq(lD);
+            expect(stateVariables["/lE"].stateValues.value).eq(lA);
+            expect(stateVariables["/lF"].stateValues.value).eq(lF);
+            expect(stateVariables["/lG"].stateValues.value).eq(lG);
+            expect(stateVariables["/lH"].stateValues.value).eq(lC);
+            expect(stateVariables["/lI"].stateValues.value).eq(lI);
+            expect(stateVariables["/lJ"].stateValues.value).eq(lJ);
+            expect(stateVariables["/lK"].stateValues.value).eq(lD);
+            expect(stateVariables["/lL"].stateValues.value).eq(lL);
+            expect(stateVariables["/lM"].stateValues.value).eq(lM);
+        }
+
+        let lA = "A",
+            lC = "C",
+            lD = "D",
+            lF = "F",
+            lG = "G",
+            lI = "I",
+            lJ = "J",
+            lL = "L",
+            lM = "M";
+
+        await check_items({ lA, lC, lD, lF, lG, lI, lJ, lL, lM });
+
+        lA = "N";
+        await updateTextInputValue({ name: "/tiA", text: lA, core });
+        await check_items({ lA, lC, lD, lF, lG, lI, lJ, lL, lM });
+
+        lA = "O";
+        await updateTextInputValue({ name: "/tiB", text: lA, core });
+        await check_items({ lA, lC, lD, lF, lG, lI, lJ, lL, lM });
+
+        lC = "P";
+        await updateTextInputValue({ name: "/tiC", text: lC, core });
+        await check_items({ lA, lC, lD, lF, lG, lI, lJ, lL, lM });
+
+        lD = "Q";
+        await updateTextInputValue({ name: "/tiD", text: lD, core });
+        await check_items({ lA, lC, lD, lF, lG, lI, lJ, lL, lM });
+
+        lA = "R";
+        await updateTextInputValue({ name: "/tiE", text: lA, core });
+        await check_items({ lA, lC, lD, lF, lG, lI, lJ, lL, lM });
+
+        lF = "S";
+        await updateTextInputValue({ name: "/tiF", text: lF, core });
+        await check_items({ lA, lC, lD, lF, lG, lI, lJ, lL, lM });
+
+        lG = "T";
+        await updateTextInputValue({ name: "/tiG", text: lG, core });
+        await check_items({ lA, lC, lD, lF, lG, lI, lJ, lL, lM });
+
+        lC = "U";
+        await updateTextInputValue({ name: "/tiH", text: lC, core });
+        await check_items({ lA, lC, lD, lF, lG, lI, lJ, lL, lM });
+
+        lI = "V";
+        await updateTextInputValue({ name: "/tiI", text: lI, core });
+        await check_items({ lA, lC, lD, lF, lG, lI, lJ, lL, lM });
+
+        lJ = "W";
+        await updateTextInputValue({ name: "/tiJ", text: lJ, core });
+        await check_items({ lA, lC, lD, lF, lG, lI, lJ, lL, lM });
+
+        lD = "X";
+        await updateTextInputValue({ name: "/tiK", text: lD, core });
+        await check_items({ lA, lC, lD, lF, lG, lI, lJ, lL, lM });
+
+        lL = "Y";
+        await updateTextInputValue({ name: "/tiL", text: lL, core });
+        await check_items({ lA, lC, lD, lF, lG, lI, lJ, lL, lM });
+
+        lM = "Z";
+        await updateTextInputValue({ name: "/tiM", text: lM, core });
+        await check_items({ lA, lC, lD, lF, lG, lI, lJ, lL, lM });
+    }
+
+    it("label, labelIsName and copies, start with label", async () => {
+        const doenetMLForA = `<point name="A"><label>A</label></point>`;
+
+        await test_label_labelIsName_copies(doenetMLForA);
+    });
+
+    it("label, labelIsName and copies, start with labelIsName", async () => {
+        const doenetMLForA = `<point name="A" labelIsName />`;
+
+        await test_label_labelIsName_copies(doenetMLForA);
+    });
+
+    it("label, labelIsName and copies, copy in labels", async () => {
+        const doenetMLForA = `<point name="A"><label copySource="Al" /></point>`;
+
+        await test_label_labelIsName_copies(doenetMLForA, true);
+    });
+
+    it("escape underscore and caret in labelForGraph except if math", async () => {
+        let core = await createTestCore({
+            doenetML: `
+  <graph>
+    <point name="A" >
+      <label>x_1</label>
+      (0,0)
+    </point>
+    <point name="B" >
+      <label><m>x_1</m></label>
+      (1,1)
+    </point>
+    <point name="C" >
+      <label>x^1</label>
+      (2,2)
+    </point>
+    <point name="D" >
+      <label><m>x^1</m></label>
+      (3,3)
+    </point>
+    <point name="E" >
+      <label>x^1 or <m>x^2</m> or x_3 or <m>x_4</m></label>
+      (4,4)
+    </point>
+    <point name="F" >
+      <label>x_a^b or <m>x_c^d</m></label>
+      (5,5)
+    </point>
+  </graph>
+
+
+    `,
+        });
+
+        const stateVariables = await returnAllStateVariables(core);
+        expect(stateVariables["/A"].stateValues.label).eq("x_1");
+        expect(stateVariables["/A"].stateValues.labelForGraph).eq(
+            "x&UnderBar;1",
+        );
+        expect(stateVariables["/B"].stateValues.label).eq("\\(x_1\\)");
+        expect(stateVariables["/B"].stateValues.labelForGraph).eq("\\(x_1\\)");
+        expect(stateVariables["/C"].stateValues.label).eq("x^1");
+        expect(stateVariables["/C"].stateValues.labelForGraph).eq("x&Hat;1");
+        expect(stateVariables["/D"].stateValues.label).eq("\\(x^1\\)");
+        expect(stateVariables["/D"].stateValues.labelForGraph).eq("\\(x^1\\)");
+        expect(stateVariables["/E"].stateValues.label).eq(
+            "x^1 or \\(x^2\\) or x_3 or \\(x_4\\)",
+        );
+        expect(stateVariables["/E"].stateValues.labelForGraph).eq(
+            "x&Hat;1 or \\(x^2\\) or x&UnderBar;3 or \\(x_4\\)",
+        );
+        expect(stateVariables["/F"].stateValues.label).eq(
+            "x_a^b or \\(x_c^d\\)",
+        );
+        expect(stateVariables["/F"].stateValues.labelForGraph).eq(
+            "x&UnderBar;a&Hat;b or \\(x_c^d\\)",
+        );
+    });
+});
diff --git a/packages/doenetml-worker/src/utils/label.js b/packages/doenetml-worker/src/utils/label.js
index 89a7699d0..da79228bf 100644
--- a/packages/doenetml-worker/src/utils/label.js
+++ b/packages/doenetml-worker/src/utils/label.js
@@ -1,3 +1,14 @@
+export function returnLabelAttributes() {
+    return {
+        labelIsName: {
+            createComponentOfType: "boolean",
+            createStateVariable: "labelIsName",
+            defaultValue: false,
+            public: true,
+        },
+    };
+}
+
 export function returnWrapNonLabelsSugarFunction({
     wrappingComponentType,
     createAttributeOfType,
@@ -203,6 +214,10 @@ export function returnLabelStateVariableDefinitions() {
                 dependencyType: "shadowSource",
                 variableNames: ["label", "labelHasLatex"],
             },
+            unlinkedCopySource: {
+                dependencyType: "unlinkedCopySource",
+                variableNames: ["label", "labelHasLatex"],
+            },
         }),
         definition({ dependencyValues, essentialValues }) {
             let labelChild =
@@ -240,20 +255,22 @@ export function returnLabelStateVariableDefinitions() {
                 // find a valid name for a label from the component name
                 // or the name of one of its shadow targets,
 
-                let label = "__";
+                let label = "_";
                 let cNames = dependencyValues.componentNameAndShadowSourceNames;
 
                 for (let cN of cNames) {
-                    let lastSlash = cN.lastIndexOf("/");
-                    label = cN.substring(lastSlash + 1);
-                    if (label.slice(0, 2) !== "__") {
+                    let lastSlashInd = cN.lastIndexOf("/");
+                    label = cN.substring(lastSlashInd + 1);
+                    if (label[0] !== "_") {
                         break;
                     }
                 }
-                if (label.slice(0, 2) === "__") {
+                if (label[0] === "_") {
                     // if label from componentName starts with two underscores,
                     // it is an automatically generated component name that has random characters in it
                     // Don't display name, as they are for internal use only (and the user cannot refer to them)
+                    // (Nov 2024) Also now that are phasing out automatically generated names with single _,
+                    // don't display those either.
                     return {
                         setValue: {
                             label: "",
@@ -262,26 +279,22 @@ export function returnLabelStateVariableDefinitions() {
                     };
                 }
 
-                if (label[0] !== "_") {
-                    // we have a user supplied name
+                // we have a user supplied name
 
-                    if (label.includes("_") || label.includes("-")) {
-                        label = label.replace(/[_\-]/g, " ");
-                    } else if (label.match(/^[a-z]/)) {
-                        if (label.match(/[A-Z]/)) {
-                            // label starts with a lower case letter and has an upper case letter
-                            // treat as camel case and add spaces and lowercase letters
-                            label = label
-                                .replace(/([A-Z])/g, " $1")
-                                .toLowerCase();
-                        }
-                    } else if (label.match(/^[A-Z]/)) {
-                        if (label.match(/[a-z]/)) {
-                            // label starts with a upper case letter and has an lower case letter
-                            // treat as pascal case and add spaces
-                            label = label.replace(/([A-Z])/g, " $1");
-                            label = label.slice(1); // delete extra space at beginning
-                        }
+                if (label.includes("_") || label.includes("-")) {
+                    label = label.replace(/[_\-]/g, " ");
+                } else if (label.match(/^[a-z]/)) {
+                    if (label.match(/[A-Z]/)) {
+                        // label starts with a lower case letter and has an upper case letter
+                        // treat as camel case and add spaces and lowercase letters
+                        label = label.replace(/([A-Z])/g, " $1").toLowerCase();
+                    }
+                } else if (label.match(/^[A-Z]/)) {
+                    if (label.match(/[a-z]/)) {
+                        // label starts with a upper case letter and has an lower case letter
+                        // treat as pascal case and add spaces
+                        label = label.replace(/([A-Z])/g, " $1");
+                        label = label.slice(1); // delete extra space at beginning
                     }
                 }
 
@@ -304,6 +317,20 @@ export function returnLabelStateVariableDefinitions() {
                         ),
                     },
                 };
+            } else if (
+                typeof dependencyValues.unlinkedCopySource?.stateValues
+                    .label === "string"
+            ) {
+                return {
+                    setValue: {
+                        label: dependencyValues.unlinkedCopySource.stateValues
+                            .label,
+                        labelHasLatex: Boolean(
+                            dependencyValues.unlinkedCopySource.stateValues
+                                .labelHasLatex,
+                        ),
+                    },
+                };
             } else {
                 return {
                     useEssentialOrDefaultValue: { label: true },