It's his name as Emperor - Napoleon I. Before 1804 he's plain Napoleon Bonaparte. It's the same usage as King George, King Louis etc.

It should be noted that Julius was not Caesar's first name. His full name was Gaius Julius Caesar – Gaius was his praenomen, his true given name; Julius was his nomen, identifying his gens or family; and Caesar was his cognomen, an additional hereditary name identifying his branch of that family.

At the time in Britain he was never referred to as Napoleon as that would have implied recognition of his self-awarded status. If referred to in anything official he was plain Bonaparte, or General Bonaparte at best.