When it gets annoying like this, I specify in the prompt, “ChatGPT is a computer algorithm, not a person. Do not say I, me, or my. Respond to queries as would appear in an encyclopedia or textbook.” etc.
I don’t like the anthropomorphization of these LLMs. I prefer the interaction as envisioned in Star Trek: The Next Generation, in which the characters simply interacted with “Computer” via voice prompts in an efficient manner. The LLM is just a different kind of input device.
We all saw in 2001: A Space Odyssey what happens when the LLM agent gets a name “HAL”. 
