Originally Posted by
Hornetguy
Here is my understanding based upon fighter lore...
The original Red air F-16's were referred to as "Vipers" to differentiate them from Blue air F-16's, technically the F-16 is the "Fighting Falcon". Over the years the name then took for the entire group, probably for comm brevity reasons; "Kill the
Fighting Falcon arcing in a right hand turn at 16K" was too much, whereas "Kill the
Viper arcing in a right hand turn at 16K" met the intent of comm brevity!

Viper was the original name that the General Dynamics rank-and-file were pushing for the aircraft...after the "Viper" fighter on Battlestar Galactica, reportedly.
The "Fighting Falcon" name is what the USAF came up with in an internal USAF contest to "name the fighter". I believe some TSgt won with that entry.