The best explanation was that that F-117 was both a security measure and a bureaucratic shortcut. According to Paul Crickmore, the term F-117 was a way for the Tonopah pilots to record their flight hours when the Nighthawk was working up its operational readiness without revealing the nature of the low observable plane or its mission. However, there was also an overlap between the Nighthawks with another black Air Force operation: the flight testing of Soviet MiGs. These captured aircraft also had an odd designation (one MiG-17 had the designation YF-114A) for the same reason as the Nighthawk. F-117 was a means to differentiate the new aircraft from these ex-Sovier bloc aircraft. Once the secrecy about the Nighthawk was lifted, the F-117 designation stood as a bureaucratic expedient.

Sources

Crickmore, Paul F. Lockheed F-117 Nighthawk Stealth Fighter. Oxford: Osprey Publishing Ltd, 2014.

O'Connor, William B. Stealth Fighter A Year in the Life of an F-117 Pilot. Minneapolis, MN: Zenith Press, 2012.