Played in:
"Team Overkill" - so named because our usual way of dealing with *anything* (even including a single 6 h.p. Goblin) was to start chucking the multi-dice heavy-damage spells until the neighbourhood was thoroughly sterilized!
"Company of the Green Cloak" - so named because by concidence at one point every PC mini except one had been painted (either by us or by WotC) with a green cloak.
Lots of other un-named groups, sometimes referred to by where they usually adventured in the world (e.g. "northern", "eastern", etc.) or by what night the games are (e.g. "Friday", "Sunday", etc.)
DMed:
"The Enterprise Company" - so named because the local laws required all adventuring groups to have a name, and this was the best they could come up with.
"Main" and "Split" - so named because one party split off from the other. The pre-division group then retroactively got named "United". Exciting, huh?
The three groups in my current campaign have started referring to themselves as "Alpha", "Beta", and "Gamma" games but haven't actually named their parties yet; I really hope that at some point they do. That said, the all-female-PC "Gamma" group may be slowly on their way to naming themselves "Team Makeover"; we'll see.
Lan-"Team Overkill were *dangerous*, that's why I never ran with them"-efan