The correct grammar would be "The Mansion Built by No One", so I'd use that one. You could also do something like "The Mansion Built by No Man", but that's up to you. :)
I would agree that “no one” is more correct than “none”, but I wouldn’t say that “none” is entirely wrong. After all, on Star Trek: Discovery there was a Klingon character named “Voq, son of none”…
