I was in a Neverwinter Nights group called Seekers of the Light. That was the name the DM gave the campaign as well as the party, and it was related to one of our first adventures.
My current D&D group is Gorgoldand's Folly. "Follow our hapless heroes as they travel the world randomly in search of a legendary hoard of treasure." I'm not sure we've ever used that name in-character though. In one recent session we met a bard who said he was a member of an adventuring group called The Crimson Cloaks, and my character wondered why our own group didn't have a cool name like that.
The Attackers of Opportunity
Combat Reflexes
Combat Expertise
The Bull's Rush
The Cleavers
Weapon Specialization
The Whirlwind Attackers
The Black Tentacles
Dispellers of Chaos
Coup de Grace etc. etc. etc.
Johnny and the Contusions! (replace Johnny with whatever character in the party uses a mace). Now, if they were pirates, Extravaganza of the Seas would work pretty well...