I wouldn't call ChatGPT "brand recognition". People know the term ChatGPT, but I don't think they associate it with OpenAI or any company in particular, in the same way that people might associate Civic with Honda. Instead they'll associate it like they do the terms Bandaid, Kleenex, etc., as a catch-all term for LLM chat interfaces, regardless of who is providing the service. When OpenAI starts ads, I imagine people will start saying "oh, here's a ChatGPT without ads" and point to Claud or Gemini or whatever.
Given enough evidence of this, some plucky startup can get the trademark invalidated. https://en.wikipedia.org/wiki/Generic_trademark
Most people I know don't even know if it's ChatGPT or ChatTPG or ChatPGT or ChatGTP.