Hm...more than likely I'll be part of the Falco team. You know what? Go ahead and put me down. It'll be easier to lend a hand when I'm less ambiguous.
About the name though, I like the alliteration (Starwolf Squadron, Fox's Faction, that sort of thing) and I think if we went with Cobalt Avians it wouldn't really fit well.
I think the names should be the Starwolf Squadron, the Fox Force, and the Falco Faction. I won't lose sleep over it, but it makes more sense in terms of wordplay. They all have alliteration and they also match in syllables (Starwolf = 2 syllables, Squadron = 2 syllables, Fox = 1, Force = 1, etc.).
It's probably too late now, but I thought I'd give it a shot.