When my team was brainstorming team names for our Rookie year (last year!), we got everyone together and made a giant list. Every suggestion made it onto that list no matter how ridiculous until we had ~6 pages. We narrowed down some obvious no-go's like Scorpion Kickers, Meatloaf, and Brobotics. Omit anything with a copyright- Hobbit or Sonic Screwdrivers- unless you want to go through the process of gaining the rights to use that name. (I just pulled up our old list and had a good laugh about some.) We narrowed it down to four names: 5UP3RN0V4, STEMpunk, Mentally Buoyant, and Laser Shark Commando Squad.
After we couldn't narrow them down by votes, we thought about marketing and image. STEMpunk won at the agreement of all.

Because you'll want to have a team name that lasts, I think it's important to have agreement at the beginning because that consensus will most likely last if you're able to build upon an image.