You are correct. The Byzantine Empire considered itself Roman and called itself the Roman Empire. As with the Remnant, there has been no de jure change. However, the situation in reality in both situations is quite different. The Byzantine Empire was a Greek speaking Empire with a largely Greek and Thracian nobility ruled from a city in Asia Minor by a dynasty with few if any Latin connections (Emperor Justinian began as a Thracian officer and his wife Theodora was an Egyptian whore) with an army that was in the main made up of Thracian and Illyrian cataphracts whose military organisation owed little to the Roman legions but much to the Persian dehgans whose armed might was didicated to defending the most important province in the Empire which was Egypt. They were Roman only in name. And there isn't (contrary to all popular suspicion) all that much in a name. I said nothing about the Holy Roman Empire which was neither Holy nor Roman nor an Empire. To reiterate my point...what the Remnant considers itself to be is, from an external point of view, irrelevant. In the end, what it all boils down to is that if Pellaeon wants to be Grand Admiral, Head of State or Supreme High Mugwump, who's going to say no?