Loli Squad, Rainbow Bears, VRPD, etc etc etc. You've seen all the different groups. Wouldn't it be awesome if we could have WoW-style tags under our names with the group we associate with?
Ideally, I see this system working more like Wildstar's "circles", or Guild Wars 2's guids. You can join as many as you want, but you "represent" only one at a time. A nameplate mockup might look like the attached image.
You would manage the guild in-game via a simple interface much like the Social menu. If you have permission, you can invite people to your guild or remove them with the context menu. You can change which guild you're representing in your in-game UI.
Additionally, on a website (say, an extension of the vrchat.net/home page), you could manage your group from a browser. You could also upload your icon (in the form of a 1:1 ratio PNG), change your guild name, leave a group, or change your representation via this site.
The "group" would have 3 permission groups:
Administrator - Can represent the group, manage the group on the website, add members, remove members, change group icon, change group name
Officer - Can represent the group, can add members, remove members
Member - Can represent the group
Furthermore, allowing Playmaker access to "guild ids" (such as "current guild represented") would allow people to create rooms with permission-based colliders-- maybe to set up private areas for setting up Improv for those in the improv group, allowing people behind the bar in the Pug, etc.
Apologies if this is too long! This is an exciting idea to me, and I think it would be very heavily used.