The Telecaster (the two pick-up-version of Fenders first model Esquire) was originally called Broadcaster. But as Gretsch had a line of drums called Broadkaster, they claimed that Fender violated their trademark. The Broadcasters with the name removed and the guitars produced before Fender came up with the name Telecaster are now known as Nocaster. Fender has actually trademarked that name and are now producing Nocaster replicas.

The first Fender Precision Basses had a shape like the Telecaster, but when it was updated a few years later to resemble the new Stratocaster, the original was renamed Telecaster Bass.

The SG was originally also called Les Paul, as the design was made as a more easily playable version of the original (thinner flat body, double cutaway). But Les Paul himself didn't like the new design and asked for his name to be removed.
SG stands for Solid Guitar. (The name of the bass-version, EB, stands for Electric Bass.)