I attempted to read the wikipedia page, but it just confused me further. What were cognomans, and what could we relate them to nowadays besides a nickname? Were they used in an individual's official name?
If I had to pin-point this to a specific period, I would be interested in the naming customs of the Julio-Claudian dynasty, or just after the rise of the Roman Empire.
hi! FYI, there have been several posts asking about Roman naming conventions, so you may find additional info of interest in these:
in general
a few scenarios
some specific names
Why were Roman Emperor's obsessed with having Caesar in their name?
Why is the name Flavius a sign of social status in the Late Roman Empire? ... although be aware of this one Why did virtually every Roman Emperor from Constantine I to Heraclius (c. 300CE-600CE) have the name Flavius? Had Flavius become the new Caesar?
Was Galen (Aelius Galenus) a member of the gens Aelia or not?
We can't really compare cognomens to anything we use today in the say, North America, because we don't have an equivalent. The cognomen essentially arose because Romans just didn't have that many names to spread around. Literally, their language just had a small, finite amount of names to give, so you had to find a way to distinguish members of the family. That's where the role of the Cognomen comes in.
Now you could say we have something kind of like that in the West today, when you get nicknames that have very little bearing on their actual name, like Butch or when people have "funny" or assumed middle names, but that's still kind of a stretch. We don't run into the need to distinguish with a cognomen because we aren't running out of ways to identify people.
In the Julio-Claudian era you're referring to, and around Caesar's time, the cognomen is used by us today to help distinguish the people of the time. Generally speaking the rules for how you address the individual depends heavily on the formality of the circumstance. If you are a close friend of Caesar's and trying to get his attention at a small family gathering you'd likely call him Gaius, Julius, or Gaius Julius. If you are addressing him, you should refer to him as Julius Caesar, or G. Julius Caesar, out of respect.
The easiest way to remember how Roman names worked is this:
Gaius is his personal name, meant for informal occasions, meant affectionately among people he trusts outside of decor. You would not walk up to the President and call him Barry, so you shouldn't walk up to Caesar and say, "Ave, Gaius!"
Julius is his family/clan name. He shares this with plenty of other people. It helps indicate bloodline and distinction. Calling out a name like "Julius" or "Publius" will cause half of Rome to go "Eh?"
Caesar is his cognomen, which separates him from other Gaius Juliuses of his day.
Later they started adding more and more names, but the principle remains largely the same.