Only in the same way the nano editor should rename itself to Stable Diffusion because of Google naming their image generator nano-banana.

Gemini predated Google's Gemini by many years and was a sufficiently known project. Google hijacking known project names is a thing which keeps happening for some reason.

or the gemini protocol chose a really overloaded name, even if you just count tech: https://en.wikipedia.org/wiki/Gemini