Why did the use of the family name (Cognomen), as one's surname, diminish and nearly disappear entirely during the 4th - 11th centuries throughout the Eastern Roman Empire?
Brief history of the early existing Roman naming practices of the Principate Period (27 BC – 284 AD)
According to Christopher Andersen (1977), the ancient Greeks, Hebrews, and Romans had surnames. After the fall of the Roman Empire, however, surnames disappeared until the eleventh century.
NOTE: In the text above, Christopher Andersen was strictly referring to the Roman Empire which would have been a predecessor to the Byzantine Empire (Eastern Roman Empire | 330 AD to 1453 AD).