Yeah, can't name something after its component ingredients, that's madness. Let's set up a ban on chicken parmesan, spaghetti bolognese and common smurfing sense.
What the hell is chicken parmesan?
I'm gonna hazard a guess at chicken with parmesan.
You use parmigiana, which is the common name for the sauce, not parmesan, which is the common name for the cheese. This is why you don't let english people name things.
Moral of this thread; Brits have silly names for everything.