Pretty sure OpenAI copyrighted the "GPT" suffix, so not sure what Kagi is naming an API this. I think OSS projects get a pass, but I'd imagine commercial competitors.
edit: copyright -> trademark
Based on the context provided:
OpenAI has applied for trademarks containing "GPT" with the US Patent and Trademark Office (USPTO) in recent years, including:
"GPT" in December 2022 [[1]] "GPT-5" in August 2023 [[2]] However, it is unclear if the USPTO has approved or rejected these applications. Some sources suggest OpenAI's application to trademark just "GPT" alone may be rejected, as it is a generic term. [[3]]
OpenAI communicates they do not permit use of "GPT" in product or app names, as it could confuse users. [[4]] However, others argue it may not affect ability to build similar models, just prohibits using the name. [[5]]
In summary, OpenAI has sought trademarks on "GPT" terms, but their status is uncertain. I do not have enough information to confirm if "GPT" itself has been fully trademarked.