I'm not clear why you mention Groups, and Administrators in particular, when you seem to be talking about changing User Names.
I confess to never having trying to change my User Name on a forum where I am sole Administrator and there may be locks in the software that prevent you from doing that.
But, with that possible exception, any Registered user can change their own User Name by going to their "Account Setting screen and editing the fields under "Edit Personal Information".
Changing Group names is different. There is no facility for that. However, there is a work around. You can create a new group, with the desired name and cut/paste across all the users from the old group. When a Group has has its last member removed and the edit saved, the group itself is removed from the system.
Volunteer Helper - but recommending that users move off the platform!
Once the admin for GregHelp now deleted.