The Roman form of naming was pretty logical and limited. A name was made up of the praenomen, the nomen and the cognomen. The nearest analogies today are that the praenomen was the personal or christian name, the nomen was the tribe/clan name and the cognomen was the surname within the tribe/clan.

So to use some well known examples; Marcus Tullius Cicero. The praenomen for Cicero, of which there were about a thousand all up, was Marcus. Tullius was Cicero's family or clan name - the nomen. Which could be traced back to Regal Rome. The cognomen was often a common word, like rabbit, or a plant etc - Cicero means chickpea. In the ribald rhetoric of Roman politics the cognomen was often a source of mockery or insinuation. The closest anglicized version of Cicero's name is Marcus Cicero of the house of Tullius.

The Romans also added names, called agnomens, to the end of their formal name to denote triumphs. A good example is Publius Cornelius Scipio Africanus. Africanus was added to his name (by himself) in honor, and reminder, of his defeat of the Carthaginians.

Another example of the complexity of Roman names is Julius Caesar, the first dictator for life, and Augustus, the first emperor of Rome. The Roman name for Caesar was Gaius Julius Caesar. Augustus was his adopted son through Julius Caesar's will; but Augustus was born Gaius Octavius. Not all Romans had a cognomen. Probably the anglic equivalent of not having a middle name I guess ... (I don't have a middle name) and seen as unusual.

Augustus' father, after his praetorship, put down a slave revolt in Thurii. As a result he took the honorific (like Scipio did with Africanus) which was added to his name and automatically to his sons'. So the future Augustus became Gaius Octavius Thurinus.

Years later he was named in Julius Caesar's will as his heir, so the future Augustus became Gaius Julius Caesar Octavianus which denoted he was now the son of Caesar but from the Octavius family/clan/tribe. Augustus, as we know him today, is an honorific which was granted by the Roman Senate, which rather than being a constitutional position, is a religious one.

One of the confusing parts of Roman names is that there were so few praemonens. To make it more difficult for historians, it seems the first son always took the praenomen of their father. The lex repetundarum which was a judicial roll, required that juror's names be taken down in the form: father, tribe and cognomen. Presumably the taking down of the father's name was due to the Roman organisational form of the paterfamilias which gave the father complete sovereignty over his family and property. Rome was a male dominated world.