I have in my mind, when used in this context in historical writing, they are usually just called "appellations". However, I'm sure "sobriquets", or "bynames", would also be used to break up the monotony.
Ivan III: "Ivan The Great"
"It may be that the excessive cautiousness of his character, the lack of élan and glamour, and the very dullness of the man have prevented historians from universally recognizing
the appellation of “the Great,” first attributed to him by the Austrian ambassador to his son’s court."
http://www.britannica.com/biography/Ivan-III
Vlad III, Vlad III Dracula, "Vlad the Impaler"
"It often has been thought that Stoker based the title character of
Dracula on Vlad. Though Stoker’s notes for the novel do include mentions of “Dracula,” the historical account from which the notes were taken mentions only
the appellation, not the deeds for which its bearer was known. Some scholars have speculated that Stoker’s conversations with a noted historian, Hermann Bamburger, may have provided him with information on Vlad’s violent nature, though there is no concrete evidence to support that theory."
http://www.britannica.com/biography/Vlad-III
Diophantus "of Alexandria",
(flourished c. AD 250), Greek mathematician, famous for his work in algebra. What little is known of Diophantus’s life is circumstantial. From
the appellation “of Alexandria” it seems that he worked in the main scientific centre of the ancient Greek world; and because he is not mentioned before the 4th century, it seems likely that he flourished during the 3rd century.
http://www.britannica.com/biography/Diophantus-of-Alexandria