Uhh... the United States Justice system? Prior art is morally nice but ultimately meaningless unless a judge agrees with you, which can cost a lot of money before you get there, if you get there.
>LIVE/APPLICATION/Under Examination
>The trademark application has been accepted by the Office (has met the minimum filing requirements) and that this application has been assigned to an examiner.
Which, apart from some grammatical confusion, is pretty clear. It looks like they have GPT-3, but GPT, ChatGPT, and GPT-4 are all still pending.
https://tsdr.uspto.gov/#caseNumber=97733259&caseType=SERIAL_...
However, "GPT" itself is a type of technology (albeit one that was invented by OpenAI). It involves much more than just ChatGPT...even if we just look at OpenAI's own other offerings (e.g. GPT-1, GPT-2, Dall-E, etc.).
The "GP" (generative pretraining) has been a concept in machine learning for many years. The "T" (transformer architecture) was invented in 2017. Thus, the issue for the USPTO will be whether or not combining the "GP" with the "T" is too descriptive or even inherently generic to be "distinctive" to OpenAI.
Sometimes, general terms can become trademarks, by becoming "distinctive" to one company. Microsoft was able to do it with "Windows" (in the field of software, of course). And "booking.com" was able to trademark the word "booking" (for reservation services) in certain contexts. The issue will be whether OpenAI can successfully make the case that they've achieved something similar for the term "GPT" itself. I really remain doubtful of that, given the term's frequent usage as being a type of LLM and a general framework for generative AI.
All that said, I suppose we'll all know for sure soon enough...when the USPTO decides.