We call the Eastern empire Romans because that is what they called themselves. They were hoi Romaioi. The word "Byzantine" is a modern appellation.
Odoacer was not the first strongman to rule what was left of the West, but he was the first to dispense with the tradition of having a Roman figurehead nominally govern on his behalf. He was technically a client of Julius Nepos, but this fiction had become strained to say the least. Odoacer ruled directly with the blessing of the Emperor Zeno and even supported him when he fought the rebel Illus.
Odoacer was also really only the king of Italy. His rule did not mark the end of Roman institutions, laws, and traditions: the Ostrogoths were very Romanized and had been so for at least a hundred years. But the king of Italy had no real authority in the former provinces of the West. Carthage and North Africa were already ruled by Vandal kingdoms, Honorius had officially retreated from Britain decades before, and Spain and Gaul had both fallen. So the empire in the West was gone before 476, and what Roman authority remained in Italy wasn't even directed by Romans.
The history of Italy after Theoderic is especially interesting. The Eastern empire under Justinian launched an enormous reconquista, first taking back Carthage and North Africa and then fighting the Goths in Italy. After 20 years of terrible war, plague, and depopulation, Justinian succeeded and restored Byzantine rule in Italy. Just in time for the Lombards to invade. They defeated what was left of Greek rule almost without resistance and established their own kingdom. In AD 574 they assassinated their king Cleph (perhaps with Byzantine instigation) and Lombard rule fell apart. There followed a lengthy interregnum known as the "Rule of the Dukes." 7 Lombard dukes battled it out for supremacy of Italy while the beleaguered Byzantines maintained a foothold in Ravenna.
Interesting times. Due to war and the Justinianic plague, the population of Rome fell from about 500,000 to about 30,000.
Last edited by Maeglin; 08-24-2013 at 10:48 AM.