So, I have a question. We all know that from Oblivion to Skyrim, the CoC fully transforms in looks, personality, and voice to the Sheogorath from SI, this leaves me with just two questions:

1) When the player first gained the title of Sheogorath at the end of SI would the citizens have noticed it was someone else? What about the Saints and Seducers, Haskil? If they wouldn't notice the difference, what do they think happened to Sheogorath's champion?

2) We see the full metamorphosis complete in Skyrim. Question is, though, is the CoC now just an exact copy of Sheogorath, but still technically a different person from (I believe his name was) Ardun Sul, the original Sheogorath, or did this transformation somehow nullify the CoC and actually turned him into the Sheogorath from SI, instead of a perfect copy?

1, I think the idea was that for the residents of SI that even if they notice the difference they don't care. it doesn't matter how Sheogorath looks. He is a daedra prince, he could look any way he likes, and he really isn't known for consisteny. So I think while they had noticed that Sheo looks different, they also knew that s/he IS filling in the position of Sheogorath and is mantled with his power, meaning s/he is basically fitting to the definition of Sheogorath.
Haskill I think must be more aware of the change, but Sheogorath is as much of a position (as the Prince of Madness), as a person, and Haskill serves the position as much as the person behind it. For him, if someone fills the position, then s/he is Sheogorath, and the rest doesn't matter.

2, the CoC is now both the old Sheogorath and a new person. He still has the original CoC's memories - as Sheo mentiones them in Skyrim, but he also has the old Sheogoraths memories, and personality. i think he must be a mix between the two, in a peculiar way. Maybe Arden Sul was not THE Sheogorath, just one embodiment of Sheogorath. Sheogorath is maybe more like an idea bought into life by those who embody him, first Arden Sul, now the CoC, and when the CoC leaves, whoever comes after him. And all of them will be the same Sheogorath, only with a few new traits and memories.