Wikipedia says Caesar Augustus was born Gaius Octavius Thurinus, making his nomen Octavius and that nomen would have held sway prior to his ascension to emperor.
Screenwriters, though, seem always to refer to him as "Octavian" at that time of his life. A classicist I know assures me that his actual name after he had been adopted into the Julii was "Octavianus."
So, was that name ever used and, if so, when and for what reason(s)?
In the idealized system of the tria nomina, the form it had around the end of the Republic and the start of the Empire, the nomen indicated what clan (gens) someone belonged to. It was the most important part of the name, since it tied them into a larger family.
The man who would later be known as Augustus was born into the fairly obscure and unimportant plebeian gens Octavia, giving him the nomen of Octavius from birth.
When someone was adopted, they entered into a new gens, and thus took on a new nomen (and cognomen if applicable). When Caesar adopted Augustus, the latter replaced his own nomen with Julius, and his own cognomen with Caesar.
Then, to indicate one's birth family, pre-adoption, the custom was to take the original nomen and add the ending -anus "related to", using it as an additional cognomen. So he became, officially, Gaius Julius Caesar Octavianus.
Historically, of course, he wouldn't have been called Octavianus until he was adopted and became Julius. Using Octavianus or "Octavian" earlier in his life is an anachronism to make it clear who's being talked about, since Roman names can be confusing to people who aren't used to them.
If you're asking "when and why did he also have the name Octavianus?", your friend and Draconis gave you the answer.
If instead you're asking "in what contexts was he called Octavianus, once he gained this name?" the answer is that probably only his enemies, or at least those who weren't exactly allies, called him like that: it's safe to say that he didn't want his modest origins to be highlighted, while his enemies obviously did (notably Mark Antony*). Besides, among the tria nomina the informal one is the praenomen - so after he became Imperator, and later Augustus, virtually no one called him Octavianus. His close relatives (well, at least his wife Livia) may still have called him Gaius, close friends either Gaius or Caesar. After becoming Augustus, everyone else called him Divus Augustus.
Going on a tangent, it is interesting to note that by the start of the 2nd century AD, the informal name had become the cognomen, due to the extreme scarcity of praenomina faced with the population explosion, which had made them quite impractical.
*EDIT: As a matter of fact, Suetonius tells us that Antony went even further, calling him Thurinus with disdain - this was his original cognomen, though not even Suetonius is sure about the origin of it.
It was instead Cicero, and presumably other similar republican figures, who called him Octavianus - it makes sense for him to refer to Caesar's adoption, because Cicero hoped young Octavius could be manipulated to restore the Republic, and had a great respect for Caesar.
