Yeah, the group I run for is currently "The Blinkstone Companions" (as Blarg said), but I have a feeling that might change - since the current group is actually two groups merged together. Blargney actually gave the other group their name - "Lear's Lackeys", after the wizard who supposedly lead the party. Now the Lackeys and the Companions are together, we'll see where it goes.
I've rarely seen named groups, though I remember an FR group had a name in our 2e days. I think it was something to do with Feather Falls - the base of our group. In another 2e group I ran in (or was I a player? I forget) the group had a wagon that had been converted into rooms and extra carrying capacity, and the group was sort of referred to as "The Wagon Group". Doubly fun because they refused to leave the road. (They also had a talking horse that wound up being a pretty fun NPC).