Why do you guys need a name/patch, can't you just be a group of friends that go to games together? Honestly too many people put emphasis on the team rather than the individuals associated with it, I see you guys are young and probably new to the sport, don't worry so much about having a team name, and getting noticed and what not, honestly a lot of people will think it just makes you look like tools/posers. Just go to games, meet people, contribute to the forums and you will have a much better time.
I think most of the teams that I respect are just good groups of friends that like to play some airball together, their names aren't some crap they thought of while playing Call of Duty and they dont use stupid ass call signs or anything. If you want to have a name to associate yourself by or a patch make it original and don't put to much emphases on it.
On the other hand if you want to go all out and make yourself a specific them/unit from something then by all means do so, I've seen it done and its pretty cool, but please put some work into it, don't just throw together the shit you have laying around in your closet, buy some Ushankas online and call yourself a Russian unit or something stupid.