From many of my studies on the Roman/Byzantine Empire, I have observed that in the span of 350 years from the 'Fall of the West' to the start of the Byzantine recovery in the early 800s, almost no family names are recorded in chronicles, letters, etc. You have a whole plethora of Late Roman names like Galla Placidia and Flavius Aetius in the 5th Century, then a long period of time where people are almost universally referred to by their first name + ethnicity, place of birth, epithet, or profession (Theophanes Confessor, Paul the Deacon, Charles 'Martel', Leo III the Isaurian), and then, in the early 9th Century, a return to continuous family names again (Michael I Rangabe, son of Theophylact Rangabe, Nikephoros Phokas the Elder, and Michael Melissenos, to name a few).
What I'd like to know is: what actually caused this to happen? Was the elimination of the familial name an artificial construct brought about by the style of chronicling (meaning that the names still existed, but were simply not recorded), or was it part of the wider cultural, economic, or political changes that occurred during the era, meaning that people simply had no use for, or perhaps forgot, their old family names?
And one final question: is there much evidence to support the idea that some of these 'new' Medieval surnames were originally taken to honor or support famous religious leaders of the time, such as Popes or saints?
I actually talk about this extensively in the below link, which includes a nice JSTOR citation for further depth.
The tl;dr of it is, the social system that privileged documented patrilineal descent for office-holding vaporized during the chaos, collapse, and reformation of eastern Roman society into the Byzantine society in the 100+ years of conflict Constantinople had with first the Sassanids and then the Arabs, as society shifted from aristocracy to "meritocracy" (obviously nothing's purely meritocratic, but during the 7th century crisis, military capability trumped ancestral prestige). Surnames reappeared once the aristocracy made a come back, after Byzantium stabilized and was able to go back on the offensive.
For more information, check out (of course):