Why choose the name Copilot when that's already the name for products built by AWS, Microsoft, and GitHub?
In all seriousness though, you could end up being liable for diluting their trademark, and if you aren't set up in a corporation, the liability could hit you personally.
I'm not a lawyer anymore, but this is the sort of thing that sets off all kinds of alarms in my head. This looks like a cool project, and it would be unfortunate if it got mired down in legal controversy — especially if that was totally avoidable.