Humpy,
If you want to rename in such a fashion, you still can't lose the "F" even if that just refers to a pretty effective self-escort capability. After procuring AIM-120, the first time we stuck even just a couple of guys toting slammers into a bomber package, Red Air had to completely change its game plan and the results were very different from sending in just a bunch of bombers. That difference is amplified many times if Red can't even see them at range and the whole package can shoot. Ah, happy days of low level COMAO!
The same would be true (hopefully for the RN) using F-35 as fleet defence. It may not be the best fighter in the world (no, I'm not getting into that argument at the moment), but having it there with A-A mx as a hard to see part of an integrated AD system is still going to make a very big difference. Dare I say it, better than Sea Harrier and infinitely better than the thing that followed it, i.e. nothing.
So, if you really feel strongly about it, F/A-35 might be more appropriate.