???
It's stored by the number in the tables... isn't it? Changing the name won't affect access of those who belong to that group, or the forums they have access to <img src="https://www.ubbcentral.com/boards/images/graemlins/smile.gif" alt="" />
Renaming the group doesn't change other settings, only the name. Those who belonged to Group Superman will still have access to the same stuff even if you change the name to Group Kryptonite <img src="https://www.ubbcentral.com/boards/images/graemlins/smile.gif" alt="" />
