What was the name of the Eastern Roman Empire after the partition?

It began to be called the Romei state, and also its name was “Byzantium”. It existed from 395 to 1453. The exception was the period from 1204 to 1261, when Constantinople was the capital of the Latin Empire, and the Nicene and Trebizond empires lived separately from it. The heyday of Byzantium was the middle of the 6th century. In 1453, the already very weakened Byzantium was conquered by the Ottoman Turks, in 1461 they captured Trebizond.