It's called the "United Federation of Planets". But can a society located on something other than a planet (e.g. moon, asteroid, space station) become a member?
By "member", I mean that it is directly called such, or it has representatives in the Federation Legislature. Societies that are merely colonies or protectorates don't count (but may later become members).
Planets may not be fully settled, or have factions that aren't part of the Federation. For the purpose of this question, they're still considered to be "on a planet" and therefore don't count.
Canonical sources (TV shows and movies) only, please. Memory Alpha is not canon, and their list of Federation members appears at first glance to be all planets anyway.