Most of the groups I play with end up namaing their group, generally after the first few games.
I've been part of the Warriors of Dawn, the Raiders of Rappan, the Five, the Six (unrelated, oddly), the Heratics, the Loyal Opposition, the Matadores of Maya, and the Spellknights, just off the top of my head.
Normally names come up in play, often when we're joking around over pizza.
I think it adds a sense of community among players,. which is important to getting the right feel for a game.