I was under the impression that with Antony's defeat at the battle of Actium and his eventual suicide in Eygpt Octavian had all records of him destroyed, along with the banishment of his name - essentially an attempt to erase him from the history books.

I don't really know what would give you that impression. Even had Antony undergone damnatio--a punishment that did not exist yet until Tiberius in its very earliest form--the purpose of damnatio was not systematic extermination of a person's existence, but the condemnation of his legacy.

Antony would have been extremely difficult to erase. Most of the prominent writers of the Augustan Period had been if not aligned with Antony then sympathetic to him. Most importantly, Pollio was an Antonian, and it was on Pollio especially that later sources relied. Moreover, Antony had never been entirely condemned without qualms. Suetonius tells us that Bononia, for example, was excused from supporting the Actium campaign because of Antony's patronage. And Augustan literature made a major point of laying the war on Cleopatra's lap, thereby turning it into a foreign war and not a civil war. Where Antony was included in the blame it was as a puppet of Cleopatra, the real mastermind behind Actium. Already by the end of Augustus' life Antony was heavily rehabilitated, and the emperors Claudius and Caligula were descended from Antony through Drusus' marriage to Antonia, daughter of Octavia and Antony.

We know about Antony because he's everywhere in ancient literature. If the ancient historians and biographers weren't enough--he's a major figure in Appian, Dio, the Periochae of Livy (as the books themselves no longer survive), Suetonius, and Velleius Paterculus, he's mentioned in Caesar, and Plutarch has an entire biography of him--the Augustan writers all mention him, and long before Augustus' importance Cicero already talks about him.