(Counting Julius Caesar here too as a sort of proto-emperor.)

A lot of Roman Emperors, and especially the early Julio-Claudians, had very similar names. So for instance, the full names of the first few emperors (again, counting Julius Caesar) were Gaius Julius Caesar, Gaius Julius Caesar Octavianus, Tiberius Julius Caesar Augustus, Gaius Caesar Augustus Germanicus, and Tiberius Claudius Caesar Augustus Germanicus. And more than one of these people had the name "Nero" in there somewhere before taking office, despite none of them being the emperor we currently know as "Nero".

Even worse, some of those names were actually titles, or became titles later on. So for example, "Augustus" is a title that every emperor took, and "Caesar" also became an imperial title (eventually, a junior imperial title).

This seems like it would be very confusing to refer back to. Modern people who need to refer to Roman emperors shorten all these names to a single one and refer to each of these people as that name for clarity, but some of the names modern people use wouldn't have worked very well for the Romans (e.g. the man previously known as Octavian can't be "Augustus" because all the emperors were Augustus). So, how did Romans living centuries later distinguish the first Augustus from whoever was currently holding the title and all the people in between? Or Tiberius from all the other emperors named Tiberius?