The name "Octavian"

[SOCL]

hmm, intersting. Would he have used the name Augustus or did he continued to name himself Gaius Julius Caesar?

Sorry, I left out the fact his name changed again to Augustus, rather as Gabinius described. In any event, he would refer to himself as Augustus, but only in formal discussions, rather as though it were a title (i.e. Res Gestae divi Augusti), but would continue being called Caesar.

Gabinius has it exact. I should have mentioned that, but Octavian before becoming Augustus used "Imperator" before his name almost as though it were a praenomen rather than a title (which would have been attached at the end of the name), hence "Imperator Caesar...(etc)", but there is no documented use during his lifetime that he ever used the name "Octavianus". Further, the information about the legal standing of adopted names seems to be nonexistant, but rather an informal way of differentiating between two persons of the same name.