Looks like they've recently applied for the trademark but they haven't got it yet. I have no idea if they will get it or not, it is just an acronym but they did come up with it.

They did seemingly position it as a generic name for this style of AI model, and other people have been using it in that fashion (eg "gpt-j"). It's usually recommended to contrast a brand name for your product with its generic name, so that the two don't become confused. Hence why scrabble is always subtitled "crossword game".

Agreed. I doubt that OpenAI's recent application seeking to trademark "GPT" will be approved. Maybe specific models/products, but not just "GPT" by itself...

To be able to register a trademark in the U.S., the applicant has to show that the proposed trademark is in fact "distinctive" of their company. The more generic a term is in its field, whether to begin with (i.e., by not becoming distinctive in the first place...), or over time (i.e., by failing to maintain its distinctiveness), the less likely it is to be registerable. And, such "distinctiveness" is notably harder to achieve and/or maintain for terms that are more generic/descriptive rather than truly unique…

In the case of "GPT," in the context of software (specifically A.I.), those letters -- particularly in that combination -- are understood to stand for things that refer to a kind of A.I. language model having certain characteristics, even though OpenAI was first to produce a (g)enerative (p)retrained (t)ransformer and they're still the most notable provider of such technologies.