I think neither the basic idea of register renaming nor solutions to do it in a way that speeds up the processor (conceptually, each register reference has to go through a logical register-physical register lookup) are so obvious that they are guaranteed to be unworthy of patenting.
If Intel had a patent on this, it must have been on some (possibly tiny) variation, though, as IBM had register renaming in hardware in 1967 (See https://en.wikipedia.org/wiki/Tomasulo_algorithm) and the POWER1 had it in 1990.
