You cannot change the name for any of the four principle user groups:
Anyone
Registered
Administrators
Members
The first two are special as the administrators of a forum have no control over who can join them, but they can control what members of those groups can do.
You can add as many additional User Groups as you wish.
I have a lot more information about User Groups and User Permissions at my GregHelp site. See:
http://greghelp.991552.n3.nabble.com/Controlling-Access-f4012840.html
Volunteer Helper - but recommending that users move off the platform!
Once the admin for GregHelp now deleted.