I'd say it's more like kleenex. Lots of people ask you to 'pass them a kleenex' when their nose is runny, but they just mean tissue. They don't actually care what the brand is. Similarly for LLMs most people may not care (or maybe they will, and it will be more like Google search), especially if they just use it via some other app that calls LLM provider APIs. My anecdata so far says early adopters try multiple LLM providers and use the best one for their use-case. No clue on what non-tech folks think though.
Exactly. One of my coworkers prefers Gemini to overcome the blank page hurdle, and he happily describe it as "the ChatGPT from Google". What does that mean for ChatGPT as a business? Nothing. Google would like people to use Gemini, but at least they retain this user and can target him with better ads, their real business. ChatGPT is just a layman synonym for LLM.
It amuses me that ChatGPT actually seems like a generic term already. You Chat with a Generative Pre-trained Transformer. Does what it says on the tin!
The USPTO agrees with you.
"[Trademark] Registration is refused because the applied-for mark merely describes a feature, function, or characteristic of applicant’s goods and services."
https://tsdr.uspto.gov/documentviewer?caseId=sn97733261&docI...