Does KH:MR have organizations?
Yes, but they are very different than that of the Kingdom Hearts series. They are called Factions on MR. Organization XIII of KH2 no longer exists in Memory Requiem.

There are two factions: The Nocturne Syndicate (dark) and The Holders of Justice (light). You may be neutral if you wish to work alone.

Choose a side! Their stances pretty much explain themselves.
After choosing, be sure to check your group's HQ!

Can I make my own organization?
No. There will always be the two factions (Holders of Justice and Nocturne Syndicate) only, no more. Having your own is completely pointless when these exists. However, we are thinking of letting people have subgroups in the future. We will let you know.