Change name of email icloud

You cannot change your primary iCloud address name, but you can create an alias which might help in your situation and let you keep your account and everything associated with it.

Add and manage email aliases for iCloud Mail on iCloud.com - Apple Support - "An email alias is an email address that conceals your actual email address from a recipient. An alias can help you manage the email you receive, and monitor the sources of unwanted messages. You can both send and receive email from an email alias using Mail on iCloud.com.

"With iCloud Mail, you can have up to three active email addresses, and you can turn an email alias on or off at any time. You can also delete email aliases that you no longer want to use. While turning off an email alias is temporary, deleting it is permanent. "

you cannot change the address of a mailadress, if you want to have a new address you'll need to create a new mailadress