Depends. How related is the name to the someone else in question?
If I were specifically named after a r*pist (btw nice to know that I can’t even type this word in a bad sense on the Blizzard forums when we now know what’s been going on in the Blizzard offices), I would probably want to change my name. Or, if my name was the same as famous bad people, like Jeffrey Dahmer… Yeah, I wouldn’t want that to stay with me. Imagine applying for a job with that name.
This isn’t my argument for changing McCree’s name. I just think “you wouldn’t change your name” is a weak argument that doesn’t really hold.
But also I did want a refund for Zarya’s alien skin because it directly represented a sexual abuser. Is this on the same level? I don’t think so. It’s more superficial, less representative. But I could take it or leave it honestly. I don’t get why you would get attached to the name when the character will be the same.