The tone and implication of the team name that you choose will be heavily influenced by exactly what the team is doing. If the name is for a serious sports team in a league, the name is probably going to be a lot more serious than the name of a pub quiz team that is devoted to serious drinking and carousing.
Sports teams have always enjoyed naming themselves after animals, but the animals so honored typically are predators. Therefore, you can find sports teams named Eagles, Lions, Tigers and Bears, but you usually won't find any Zebras, Rabbits or Kangaroos. Even predators that don't elicit proper feelings of respect in humans, such as Weasels, Snakes and Brown Recluse Spiders, don't typically make the cut. With these thoughts in mind, here are some names you could use for your sports team: Sharks, Grizzlies, Wolverines, Badgers, Raptors, Hawks, Eagles, Cheetahs, Ocelots, Wolves, Coyotes and Lizards. A team called the Lizards would definitely get some press.
Pub Quiz Teams
Pub Quiz Night is an institution in the UK, and is slowing catching on in North America as well. Although quizzers in the UK take their quiz nights seriously, the same can't be said for their team names. Have some fun when naming your pub quiz team, and be sure that the name has overtones of excessive beer consumption. Some suggestions: Answers on Tap, The Quiz Keggers, Six Pact, Mug 'O' Brains, Drinkin' and Thinkin', Using Our Heads, The Brewmeisters and The Triviata League. Alternatively, you could create a customized name that is based on the names of the members of the team.
Bowling and Pool League Teams
Like pub quiz teams, bowling and pool league teams tend to be comprised of groups of friends or co-workers. While beer is still involved, it is perhaps consumed in somewhat less prodigious quantities than British pub quiz nights. Therefore, team names don't necessarily have to tip their hats to beer. A few timeless examples of the league team namer's art: Foley's Bowlies, Balls to the Walls, The Strikes, The 300 Boys, Rack 'Em Up, The Break Dancers, Behind the 8 Ball, Bumper Bouncers, The Cue Balls (for a team full of bald players) and Sunk on the Break.
Fundraisers sometimes organize people into teams as a means of adding excitement to a fundraising drive and creating group solidarity. These teams usually assume zany names that are designed to make people laugh and gain some attention. The best name for a fundraising team is humorous but also incorporates the purpose of the fundraising drive into the name. Some examples are Cure or Bust (for breast cancer research), Dollars for Collars (for an animal shelter), Let My People Go (to raise money for public bathrooms) and Begging for Change (advocating progressive government).