Well, if youre not adverse to having it in another country you could have this take place in some old soviet satellite state, like Poland. Then you could use the Polish
GROM , im sure they wouldnt sue you. And if they did, hey, more publicity for the game. You could still have the nuclear threat be somewhere else with an american team attempting to hande it and your GROM team infiltrating said nuclear weapons disposal area to attempt to nip the plot in the bud. As far as being the only man on the team the game could start out with your small team being inserted into the area, and then ambushed, you are knocked unconscious in the attack (good old fade to black here as your team is being cut down in a scripted event.) and you wake up with your team dead, but your team captain is missing. You think hes being held hostage or whatever, or you just think hes missing somewhere, and later he could end up not being dead but a bad guy! Yeah, plot twist! Anyway just some suggestions, I know they kinda run counter to what you said. With the game taking place in an old soviet satellite state you also get the that cool cold war, soviet feel.
Some names for the title:
Black Dawn
Shadow Ops
Ghostwalker
name of whatever ct unit you end up using, (if its fictional)
Omega Code
whatever, im just spouting off crap at this point. Ill think about it and come back later