Augustus would eventually follow the use of Imperator as a praenomen. For Caesar's precedent see Gaius Suetonius Tranquillus, Divus Iulius76Archived 2012-05-30 at archive.today: since Imperator here is a true praenomen, a translation ("commander") should—if at all—only be given for explanatory purposes. The same would apply for Divus ("god"), which derived from Caesar's god name Divus Iulius (at the latest since early 44 BC), and is therefore (as part of his name) per se untranslatable.
Suetonius, Divus Iulius37.2Archived 2012-05-30 at archive.today. In addition Cassius Dio (43.22.1) mentions elephants as part of Caesar's entourage after a banquet in Rome on the fourth day of the same triumph.
Maurus Servius Honoratus, Commentary on the Aeneid of Vergil1.267
Ludwig von Doederlein also proposed an origin from caesius, but rather interpreted it as "grey" and applied it to the color of the skin or perhaps of the eyes (Synon. III 17, mentioned in "Caesar", in Harry Thurston Peck, Harpers Dictionary of Classical Antiquities, 1898).
Augustus would eventually follow the use of Imperator as a praenomen. For Caesar's precedent see Gaius Suetonius Tranquillus, Divus Iulius76Archived 2012-05-30 at archive.today: since Imperator here is a true praenomen, a translation ("commander") should—if at all—only be given for explanatory purposes. The same would apply for Divus ("god"), which derived from Caesar's god name Divus Iulius (at the latest since early 44 BC), and is therefore (as part of his name) per se untranslatable.
Historia Augusta, Aelius2.3; Servius, Commentary on the Aeneid 1.286 i.a.; cp. Pauly-Wissowa RE X 464 sq.
Suetonius, Divus Iulius37.2Archived 2012-05-30 at archive.today. In addition Cassius Dio (43.22.1) mentions elephants as part of Caesar's entourage after a banquet in Rome on the fourth day of the same triumph.