"what model are you using, exact name please" is usually the first prompt I enter when trying out something.
> I am currently running on the Gemini model.
Gemini 1.5 Flash responds with
> I'm using Gemini 2.0 Flash.
I'm not even going to go on a limb here and say that question isn't going to give you an accurate response.
It's not unusual for AI's to think they're OpenAI/ChatGPT because it's become so popular that it's leaked into the buzz it's trained on.