If only we were so organized. Complexity classes get their name usually from the authors who invent them or occasionally by a later paper if the first paper didn't name the class or gave it an unmemorable name. Too often researchers will give a temporary name so they can work with a class and then keep that name out of laziness. Maybe I've been guilty of this a few times myself.
I could write several posts on badly named complexity classes. For now let me mention two important ones.
- NP for Nondeterministic Polynomial Time. But "nondeterministic" is not very descriptive. Logically ∃P would be better or PV for Polynomially Verifiable.
- PP for Probabilistic Polynomial Time. Since the error is not bounded away from one-half, the class is not a useful characterization of probabilistic computation. A better name would be Majority-P or just MP. BPP would then get the proper name PP and BQP would be just QP.