How to remove the Game Center and it xxxxxxnumber on my email account?

Game Centre is Built into the Operating System which resides in a Sealed and Read Only Volume which can not be Opened by the User or other " Bad Actor Software "

Period and can not be removed.

Not sure what "remove Game Center" is supposed to mean.

I don't use Game Center, but Game Center accounts are supposed to be set in System Preferences->Internet Accounts.

You want to go there and if there is a Game Center Account associated with your address, deactivate it or remove it.

It's not possible.