Setup with Custom Domain on HTTPs (Cloudflare for example)

You need at least a Shared tier App Service Plan for a custom domain

Step 1 - Add a custom domain name

Go to your webapp in the Azure portal

Click Add- Hostname

If it is a top level domain e.g. domain.com then choose an A record and follow the instructions there.
If it is a sub domain e.g. www.domain.com then choose Cname and follow the instructions there.
You have to go to your DNS provider e.g. Namecheap, GoDaddy, Cloudflare and add the records in.

You will probably want to add both sets above.

Keep hitting "Validate" every so often, but this could take up to 48 hours because DNS is annoying. Patience.

Once it validates and adds (hopefully you added everything at once , because 48 hours.)

Step 2

Go to Application Settings

and fill/add these fields in, using your domain not mine.

You should now have a custom domain with SSL (assuming you've got a cert)