There are F-105 and F-111 that are ground attack aircraft like the F-117. I think part of it was to hide the capabilities of the aircraft from other nations. Cf. SEAL Team Six
As for the F-117; fighters are generally regarded as sexier and more attractive than attack, bombers, cargo or other types. By calling it a fighter the USAF reckoned that recruitment would be easier and also that it's real purpose would be obfuscated. This is also the reason for the number; by giving a high number they indicated that this was an airplane designed prior to 1962 which never became anything.
Fascinating! Did you get any cool tours as a child?
I still never fail to get an interesting story or two from his AF days whenever we meet, though - trusting stuff like the Starfighter to a bunch of twenty-somethings is basically ASKING for lots of close shaves growing into very tall tales...