Modern Latin pronunciation is different to what it was in the past, and Octavian, to give an example, changed his name several times. Additionally, there are numerous different spellings of Roman names - is it Gaius Julius Caesar or Caius Julius Caesar? Based on this, if I was in Rome around this time, what would I call the protagonists of the era, and how would I pronounce them? How would it differ if I was, say, a friend of Caesar's and could talk to him informally, compared to if I had to address him formally like at a Senate meeting? Likewise, if I was discussing current affairs with someone, how would I refer to them?
Julius Caesar's nephew was called Gaius Octavius until he was nineteen. After he was adopted into the Julii upon Caesar's death, he became Gaius Julius Caesar Octavianus. The addition of -an- in Roman names indicates the pre-adoptive family name. HBO's "Rome" actually gets this wrong and refers to him as Octavian the whole time.