The Temptations name was created as a condition of their signing with Motown – they wanted to be called The Elgins, after a famous watch, but Berry rejected that name [[although he later resurrected it for another group) and told them to come up with something better. As portrayed in The Temptations mini series, they sat outside Hitsville throwing up all manner of names before finally settling on The Temptations.
Again, my understanding, based on what was written by Otis and Mary in their respective autobiographies, at some point Motown registered the names The Supremes and The Temptations and no doubt one or two others. Otis and Melvin were able to negotiate the return of the rights to the name when they left Motown for Atlantic, but I seem to remember they still wanted payment of some $200,000 outstanding royalties.
Eddie Kendricks briefly shortened his name to Kendrick [[without the ‘s’) as something of a protest when he discovered Motown owned the rights to his name!