Recently (as recently as the Schism storyline) the X-men split into two factions. Wolverine's X-Men (at the Jean Grey School) and Cyclop's X-men on Utopia. Are one of these 'officially' the true X-men, or do they both share/vie for the title?
Currently the comic seems to point to the Utopian group run by Cyclops as the one running under the title of X-men(series Uncanny X-Men). The only difference with this group and the original is the X now stands for Extinction. Wolverine's group hasn't done any save the world or fight with bad guys out in the open since the opening arc of the fight with Krakoa and the new Hellfire club.
Edit: After wondering around the comic shop and the marvel wiki the other day I did find more detail on this question. Specifically the characters featured in the comic titled X-men since Regenesis are based on Utopia and include: Jubilee, Warpath, Psylocke, Storm, Colossus, and Domino.
In the most recent comic Jubilee leaves this team.
Also if you looking for why all titles include the name X-men I assume it is to delineate the fact that you will be following a group of mostly mutants as they fight villains.