I am trying to think of how to put this, so if this isn't helpful I'll try another way.

Broadly speaking, a high status Roman name has three "neccesary" parts (tria nomina), but can also have honorifics attached to. In practical terms, think of Scipio Africanus, the man who defeated Hannibal. His full name would be (1)Publius (2)Cornelius (3)Scipio, and he was later granted the title (4)Africanus. "Publius" would be like a personal name ("praenomen"), the equivalent of "John" or "Robert". "Cornelius" indicates the broad family ("clan") he comes from: the "Cornelii" were a very important "clan" in Roman society. "Scipio" indicates which branch of "gens Cornelia" he comes from. "Africanus" was then added to his name after his victory in, well, Africa.

Even under the Republic this could get complicated (Publius Cornelius Scipio Africanus Aemilianus was born into the Aemilii but adopted by the son of Scipio Africanus, leading to a mouthful of a name). But when you get to the imperial period, when the emperor moght use their name to signal any number of things, it gets truly absurd.

So take Marcus Aurelius Antoninus Pius Felix Augustus. There are two emperors that might remind us of: Antoninus Pius (Titus Aelius Hadrianus Antoninus Pius) and Marcus Aurelius (Marcus Aurelius Antoninus), and this was by design because his father, the aforementioned Lucius Septimius Severus Pius Pertinax Augustus (known to us as Septimius Severus) changed his name as a way to show that he was a continuation of the previous imperial dynasty and borrow a bit of prestige from that. He is mostly known to us as "Caracalla".

This might seem a bit confusing and my only response is, yeah, it is.