Internet Account iCloud shows Apple ID, not my iCloud email address

If your Apple ID is set with gmail domain , the other two accounts should be online Change Account Information settings in Mail on Mac - Apple Support

From mail box , click on online status , the accounts should be online see Use Connection Doctor in Mail on Mac - Apple Support ( you can click take all accounts online ) .

Your primary Apple ID is say example1@icloud.com that is signed in Mac system preferences , the other web mail accounts are .

( 1 ) example2@gmail.com ( 2 ) example3@gmail.com

Any one of gmail accounts is either offline so take it online Take email accounts offline or online in Mail on Mac - Apple Support

Or it has been deleted from internet accounts you can add it .

Use your Internet accounts on Mac - Apple SupportUse your Internet accounts on Mac – Apple Support (AU)

Change Internet Accounts preferences on Mac - Apple Supportsupport.apple.com › en-in › guide › mac-help › mac

Add an internet account - Apple Supportsupport.apple.com › guide › mac-help › mac

Note : you mentioned .

I would like to change the iCloud Internet Account to reflect my iCloud email address--NOT my Apple ID--but the only field that can be edited is the description. How/where can I update the iCloud Internet Account to reflect my iCloud email address?

The Apple ID say example1@icloud.com is an iCloud mail address that is already signed in Mac system preferences and also configured in internet accounts and its reflecting .