What was Octavius's later name? I would also like to know why he is an important character
Having no legitimate children alive (his daughter Julia died in 54 BC), Julius Caesar had adopted his great-nephew Octavius as his son and main heir. Owing to his adoption, Octavius assumed the name Gaius Julius Caesar. Roman tradition dictated that he also append the surname Octavianus (Octavian) to indicate his biological family; however, no evidence exists that he ever used that name.
However, Octavius becomes later known by his most common name Augustus in 27 BC. The Senate also gave him the titles Augustus and Princeps. Augustus, from the Latin word Augere, "to increase," was a title of religious rather than political authority. According to Roman religious beliefs, the title symbolized a stamp of authority over humanity, and in fact nature, that went beyond any constitutional definition of his status. Additionally, after the harsh methods employed in consolidating his control, the change in name would also serve to separate his benign reign as Augustus from his reign of terror as Octavian. Princeps translates to "first-citizen" or "first-leader".
It is as Augustus that most of history knows this particular individual, and he is also known as the First Emperor of Rome