By what name should Octavian correctly be referred to for actions taken in 27 BCE and afterward, following the Senate's grant that year?

Explication

From 27 BCE onward, the senatorial honorific granted that year is the correct name for Rome's new ruler because it became his public identity for the rest of his life. "Octavius" belongs to his life before adoption, historians use "Octavian" for the years between adoption and 27 BCE, and "Caesar Junior" was never his title.