Every time we call something GPT we invariably would reference OpenAI's work. This tells me they don't want us to do that, and would instead like to control what can be called GPT and what cannot.
Great, they've showed their intentions and we should respond accordingly. Don't call it GPT, call it parroting (or literally whatever you want). I like this for its connection with the Stochastic Parrots work and because it is already a common usage of the word outside of ML/AI. AutoParrot, BabyParrot, ParrotAPI, etc. We train by first parroting a large natural language corpus and then fine tune the parrot model with RLHF.
Companies will do what companies do, but communities work better when they are free (as in thought).