The GMG was originally called "Homebrew Haven" - referencing "homebrewn" games, but it was changed because the word "homebrew" was too-far aligned with the home production of alcoholic beverages.
Another tidbit - why do the moderators call themselves "GMG Mike", "GMG Tim", etc? It dates back to the 1990s on AOL, where forum leaders would have specal screennames such as "AFL Rod", which stood for (AOL, or maybe Apple) Forum Leader. Al was one such volunteer, I believe his name was either "AFC Alb" or "AFL Alb" - it had to be Alb, because Al was already taken. "AFC" was often used for non-leaders, the C stood for Consultant.
The naming convention changed sometime in the 2000's when AOL began to decline. I remember Al's other screen names were "HOST MGM Al" (MGM stood for Mac GaMes) and "LDRS GAME Al", LDRS standing for leaders. The Mac Games forum was gone, so Al was just a general leader in the games forum. As a leader, Al could moderate the GameMaker message boards.
Rod Whitten was the leader of Mac Games on AOL for a very long time - as early as 1993 and probably earlier. He helped to create the GameMaker SIG on AOL - it was something special. There was even a SilverCreator message board for a time - until they decided that any inactive message board should be deleted by the system, and slowly, attrition guaranteed the demise of almost the whole of AOL's message boards, save but for rare exceptions of mostly rubbish topics.
Due to a compensation lawsuit, all remaining Community Leaders were fired several years ago and any remaining community oriented forums/message boards were removed, effectively destroying the remaining vestiges of the old AOL community.