"I looked at some possibilities last night. I like Swordmages (Defenders), because then I could create a sort of Elric character—which would seem to fit in with a drow assassin, a drow WIZard, and other elf-types. Could we be an elven contingent, Rob? Or is it better if we're a mongrel party? Or we could be mercenary outcasts and still all be elves, if it's better for us to be unaligned. Maybe we were sent to prison by a military court for a crime we didn't commit, and then we promptly escaped from the maximum security stockade to the fantasy underground. We're still wanted by the government, but we survive as soldiers of fortune. If people have problems and no one else can help, they generally let us know."
I'm partial to Acquisitions, Inc. (Dungeons & Dragons Roleplaying Game Official Home Page - Article (Penny Arcade/PvP Podcast Series 1 Ep1)). I find the construct of an incorporated private military contractor company to be very suitable for a typical D&D party's activities and motivation.
That can work, but in my opinion the best way to force the issue as a DM is to have NPCs saddle the party with an informal name they'll hate. For instance, in one group I had NPCs assume that the high Charisma bard was the party's leader; something which rankled the female players who thought of him as comically foppish. After being referred one too many times as "Liam's band", the party determinately debated the issue and finally settled upon the "Rikir Athair" or "Warriors of Life".If you want your PCs to use a group name, the easiest way to do so is to example NPCs doing the same, either currently or historically.
You sir win the thread!That's right. We are... the Fey Team.