That only means it’s not a legally recognised brand, but it is a brand nonetheless if people associate the two (and they do). A bit like the way people associate tissue paper with Kleenex, or photocopies with Xerox, or git with GitHub.
> The name Wi-Fi, commercially used at least as early as August 1999, was coined by the brand-consulting firm Interbrand. The Wi-Fi Alliance had hired Interbrand to create a name that was "a little catchier than 'IEEE 802.11b Direct Sequence'." According to Phil Belanger, a founding member of the Wi-Fi Alliance, the term Wi-Fi was chosen from a list of ten names that Interbrand proposed. (…)
> The name Wi-Fi is not short-form for 'Wireless Fidelity' (…) The name Wi-Fi was partly chosen because it sounds similar to Hi-Fi, which consumers take to mean high fidelity or high quality. Interbrand hoped consumers would find the name catchy, and that they would assume this wireless protocol has high fidelity because of its name.
The generative pretrained transformer was invented by OpenAI, and it seems reasonable for a company to use the name it gave to its invention in its branding.
Of course, they didn't invent Generative pretraining (GP) or transfomers (T) but AFAIK they were the first to publicly combine them