Couger,
I understand your feelings. I am positive beyond a shadow of a doubt, That this was NOT intentional.
The AW NightHawks are coming over as a Squad. They are not here to upset folks. They are a nice bunch of guys.
I Suggest a comprimise. Cougars Bunch Should keep there name the way it is. Its Great

The AW Nighthawks should Modify their name enough to be differnt from you. At the same time keep thier Identity
Would something like
"NtHawks Fighter Bomber Group"
Be Good enough???
Would this be a valid comprimise?
Its Very Differnt, But they dont have to Trash their heritage, WebPages and Logos.
I think its the Adult way to handle things.
Comprimise.
If you really want to change your squad to Cactus Air Force, That would be Great

We can always use more CAF in the Air

hehehehee
Seriously, We have plenty of confusion from the Canadian Air Force, Confederate Air Force, CheeseHead Air Force, and any other CAF. The Good thing is we have the Blessing of Really Cactus Air Force Guys.
The Real CAF was a group of mismatched pilots based at Henderson on Guadacanal during WWII.