Apple TV (4th generation or later) allows a custom user name, independent of your account name, legal name, or other username. Settings﹥Users and Accounts﹥[You]﹥[ᴍᴀɴᴀɢᴇ] Edit User Name for Apple TV﹥… Be as create as you want.
On smart TVs in the Apple TV app, it will instead show the name as known to Apple for that Apple ID account.
If you want to edit that, then see: appleid.apple.com﹥Sign In﹥Personal Information﹥Name﹥…
It may take some time for that edit to propagate to other devices. You may need to sign out and sign in again.
If the issue still persists, then contact Apple Support.