The team's name is the Everblades (ay how cute a play on words), and has an alligator for a mascot? What exactly is an everblade? A type of gator?

Again, another reason why I can't stand forcing names on teams due to location. If it works and sounds cool, go for it. But seriously, IMO it's ok to use a random animal or something.
IF I HAD TO go location oriented, I'd go with the Florida Mosquitoes. Can't get anymore intimidating than the #1 ranked deadliest animal. And holy Christ when mosquito season hits... (one of my buddy's football team is named the Everglades Mosquitoes, genius

)
If I could choose any name, I've always thought Vipers would make a good team name.
LOL @ the Miami New Yorkers.
