Let's be careful with terminology; there wouldn't be more than one "fork". Your question is better stated as "which side of the fork".

Nobody would "inherit" the name "bitcoin". The name would stay where it is. There aren't any kingmakers who declare who "gets the name". Perhaps in the 2017 era it was reasonable to speculate whether exchanges would swing their scepters and declare such things, but we learned that's just not how things work.

It's been almost ten years of this. I'm tired. Let's just get this fork over with, get our little airdrops and move on.