The Empire of Trebizond was one of the three Byzantine successor states that formed after the Fourth Crusade captured Constantinople in 1204, along with Epirus and Nicaea. The names of these states are all later historiographical inventions, and just like Epirus and Nicaea, the emperors of Trebizond styled themselves as "Roman Emperors" at first, claiming the ruling title for themselves and presumable they continued to refer to their state as the "Roman Empire". After Nicaea recaptured Constantinople, Emperor John II of Trebizond changed his imperial title to "Emperor of All the East, the Iberians and Perateia". Did the name of the state he was governing also change or did they continue to refer to it as "the Roman Empire"?
Also, why did they include emperor of the Iberians in their title? Is it just for the prestige of claiming descendance from the old Roman empire?