Kitty/Warhawk II is a Curtiss-Wright product..not in the airframe business anymore these days. Doesnt sound cool or contemplary enough.
Cobra II doesnt work too. The F-17 Cobra I never entered AF service.
Cougar=Ex-Navy fighter (unlikely to be adopted as name for AF plane..Corsair II ring a bell ?)
Rapier=Lame...F-22 was named Rapier at one stage.
ATF=Like the feds ? :D..I dont see the 'A' in it compared with the YF-22 and 23 just around the corner.
Puma/Panther sound too much like armoured cars.
I think Lynx is best since it is a first for fighter and cat. The westland helicopter is a british product and doesnt count.
Did we suddenly run out of names of fierce birds of prey ? Buzzard, Caracara, Kestrel, Skua, Kite..Albatross..etc