We can critic Google as much as we want, but at least it's a bit less weird to say "Hey Gemini" compared to "Hey GPT", when you know that GPT is actually something between an abstract concept and a code implementation.
See also how there's a company named 'Dr. Ing. h.c. F. Porsche AG' with a brand called 'Porsche'. But nowadays that company is just a subsidiary of Volkswagen, and they could restructure to make the Porsche AG disappear, without doing any changes to the brand.
Also, this is literally "people's car".
Had that been the case, and had the phrase been in common use, it would have been impossible to trademark "Bavarian Motor Works" to refer to part of the Bavarian motor works. But reality is different.
referring to gpt as "hey gpt" is not really different than "computer" as used in at least one popular tv show.