Please answer a question about the following article about Middle Ages:

By the end of the 5th century the western section of the empire was divided into smaller political units, ruled by the tribes that had invaded in the early part of the century. The deposition of the last emperor of the west, Romulus Augustus, in 476 has traditionally marked the end of the Western Roman Empire.[E] The Eastern Roman Empire, often referred to as the Byzantine Empire after the fall of its western counterpart, had little ability to assert control over the lost western territories. The Byzantine emperors maintained a claim over the territory, but none of the new kings in the west dared to elevate himself to the position of emperor of the west, Byzantine control of most of the Western Empire could not be sustained; the reconquest of the Italian peninsula and Mediterranean periphery by Justinian (r. 527565) was the sole, and temporary, exception.

What is another name for the Eastern Roman Empire?
Byzantine Empire