My wife and I are both 70's-80's children, so we grew up watching He-Man and She-Ra cartoons. We'd toyed with Sheba for a name, but She-Ra quickly took it's place. And yes, she believes she IS the Princess of Power.
What's interesting is, we really only use that name for command/disciplinary purposes…for some completely unexplainable reason, we've both nicknamed her "Wheatey", and I have NO idea why either of us started calling her that. We like Wheatey better, but think it's probably too late to change it as she responds to She-Ra when we need her to come, sit or stop.
So we just keep Wheatey as an "unofficial" or "nick" name.