F/A-22 is the correct name, hence "Fighter/attack" interesting, I know Nellis AFB was presumable going to be the first home base.

Mobius already responded correctly, however just to add...
The F/A designation came at a time when Congress was questioning continued funding of the program in the face of an oppinion that the Air Force didn't need a new air superiority fighter. The F/A designation was used to show Congresmen the value the plane had as a multi-role. THe airplane does have ground attack capability, however the Air Force didn't and doesn't have any intent to use it in that role.
Once the funding issues were sorted the airplane went back to being called the F-22. When it entered service it gained the "A" variant designation. F-22A is the current name.
There is talk about an F/B-22. I don't know if that will come to be more than just idle chatter. Some are of the oppinion that it's practically a done-deal (given the delay in F-35 production and the need to fill the gap with something). A "B" designation implies a very capable platform indeed.
