did he fight any wars?
Yes, the Battle of Actium.
Augustus
 The Triumvirate was eventually torn apart by the competing ambitions of its members. Lepidus was driven into exile and stripped of his position, and Antony committed suicide following his defeat at the Battle of Actium by Octavian in 31 BC.

how is the name augustus significant? As a consequence of Roman customs, society, and personal preference, he was known by many names throughout his life. after whom did he come to the throne? Julius Caesar
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Augustus [SEP] Introduction
Lepidus was driven into exile and stripped of his position, and Antony committed suicide following his defeat at the Battle of Actium by Octavian in 31 BC. After the demise of the Second Triumvirate, Augustus restored the outward façade of the free Republic, with governmental power vested in the Roman Senate, the executive magistrates, and the legislative assemblies. In reality, however, he retained his autocratic power over the Republic. By law, Augustus held a collection of powers granted to him for life by the Senate, including supreme military command, and those of tribune and censor. It took several years for Augustus to develop the framework within which a formally republican state could be led under his sole rule.