A Daedra doesn't inhabit physical space in the same sense we think of it; they are not Mundic entities. Our perception of them is conceptual, our minds display to our eyes and ears what we expect to see. So whether Sheogorath has, as a base identity, either Arden Sul or the Champion of Cyrodil, we still perceive him as Sheogorath.
At least, that's how I see it.