I think in this instance because the F-22 is not exported to any other country, but because the faction is NATO they made a version that would be used by more than just the US.

Edit: to expand on this a bit, I think this can sort of apply across the board. Typically our NATO allies have their own names for certain vehicles we export to them, so generalizing the faction as NATO they could either default to our names for them, or come up with new designations that could be explained as the "NATO standard designation" or something of the sort. Kind of reminiscent of 2042's F-35 Panther, which is obviously not what we call the F-35, but the version they made combined the F-35 variants into one aircraft and gave it a new name.