More info:
http://www.f-16.net/articles_article10.html?module=pagesetter&func=viewpub&tid=2&pid=27
Viper: the unofficial nickname
The F-16 is often referred to as the "Viper", a nickname especially popular with people involved with the F-16. Before "Fighting Falcon" was selected as official name, pilots at Hill AFB, the first F-16 base, came up with a number of proposals, including "Viper". Lt. Col. Pat "Gums" McAdoo, USAF Ret., one of the first F-16 pilots at Hill AFB, recalls the origin of the name "F-16 Viper":
At end of runway, the F-16 did resemble a cobra or something as it approached you. However, I think Northrop had already taken that name for the YF-17.
We all voted, and Viper came in really high. Seems there was a series on TV that had 'colonial Vipers' flying off of Battlestar Galactica (a term later used for the Eagle).
In any case, the Generals didn't want a plane 'named after some snake'!
Falcon was a good name, and it fit in with the motif that the Eagle had created. Sort of a little brother, but still a 'Bird of Prey'. In fact, GD had a great promo out in late 70's called "Bird of Prey", and it used the Falcon as the real world model.
Even when F-16 Fighting Falcon became the official name, Viper stuck around and became the unofficial nickname for the F-16. The name "Viper" is even officially used for the Joe Bill Dreyden "Semper Viper" award, which is awarded for excellent airmanship by F-16 pilots.