iCoud has divorced name - help I got a divorce, and my iCloud email has my old name. I did an alias, but I want that old name gone. Now what?
There are two options. The important part is to determine if you need to get a new @icloud or @me or @mac portion of the email. You can’t change that yourself.
You can change the AppleID (log in text) and everything else like name and address, just not the initial email Apple issued to your iCloud account. That portion isn’t editable any manner I’ve ever seen, and if you use a third party mail with your AppleID you can change that to a new value and leave the old email behind forever.
Assuming you can’t edit the fields you want, two options remain:

Make a new AppleID and have the other hang around for past purchases - you have to keep control of it, but not use it for primary. Make it part of the “family” if you want purchases to flow to the new account.
Make a new AppleID and just delete / leave it unused. Clean start.

I would call Apple Support or chat if any of this is unclear or confusing. Show them the exact parts you want to change before you do anything. They can advise you best since they manage the service and you don’t have to share personal details here publicly.