How to rename an admin account who has an Auth Authority?

yes, the link Change the name of your macOS user account and home folder - Apple Support explains in detail the correct way to rename your Mac. but you need to follow those instructions TO THE LETTER. making even one mistake can lock you out of the account and it will be very difficult if not impossible to recover from that. also, pay special; attention to the first step. and, of course, you should always make a backup before making changes to your Mac. and doing this is about as big as changes to your Mac get.