Dress colorfully and arrange your team symmetrically by color and call yourselves The Grey Abelians (pun on "grey aliens").
Go for mysterious: The Degenerates (my absolute favorite topic to really screw with the kids' minds when I taught Geometry)
Often taken: Pi-rates/Pi-rats of the ________
Extremely nerdy math joke (and my favorite): ∀∀ ∃∃ ("For all upside-down A, there exists a backwards E")
Integral of ex (it may be a bit too dirty to explain on this forum)
Right Hand Rulers
Tau of (your home city) or Tau-tologists
Prime cuts, USDA Primes, Prime-mates
(Hot) Chicken Proth
Sir Pinsky, Sir Cumference
Al Got Rhythm, Al Jabberwocky, Algae-Bras/Alge-Bras or Algae-Bros/Alge-Bros if you're all of one gender.
Cow Pis (I have this on a tshirt, it's a giant holstein cow patterned π with udders in the middle)
Team Doughnut, but every time it's announced correct them and say you're the coffee mugs, then apologize for an easy confusion. Swap as needed during the competition.
Axes of Evil
Eating more cheese on Thursdays.