Unable to Change Email Display Name on Mac

How about in the Mac Settings => Internet Accounts explore what you can change under the Mail accounts shown there ...?

Also see this:

Change Account Information settings in Mail on Mac - Apple Support

Add and manage email aliases for iCloud Mail on iCloud.com - Apple Support

Note that changing the full name ("alias") shown for iCloud email is slightly different as described in the above link.

Change Personal Information settings for your Apple Account on Mac

In Apple Mail, if I go to Apple Mail Settings, in the Accounts tab I see "Email Address" and entered there is shown

John Smith <john.smith@xxxx.xxx>

for a made up name of John Smith m(for purposes of illustration).

I also show the same name under my Contacts entry for me, and also for my Apple ID and iCloud in Settings for the Mac.

And that name is what shows as my email display name.

M.underwood wrote:

I see a way to change it for every email address I have *except* for iCloud/MobileMe.

Add and manage email aliases for iCloud Mail on iCloud.com - Apple Support

Without revealing my True Identity or any order personal information

For domains ending in xx@mac.com, xx@me.com or XX.icloud.com

The name preceding the @ sign

It may be derived from Apple Account

My real name is not Owl-53

My email address, preceding the @sign, was the name I used when I first setup my Apple ID account on September 18, 2005

🦉-53