The first emperor of Rome was originally named "Gaius Octavius". When he was adopted by his great-uncle, he became "Gaius Julius Caesar Octavianus". That adoption only took place with the reading of Caesar's will. Nobody, not even his mother Atia in a moment of wishful thinking, would have addressed him as "Octavian" prior to that event.
A talent of gold isn't an amount; it's measurement by weight, roughly equaling about 70 pounds. Marc Antony is given a half talent of gold, roughly 35 pounds, which he carries easily, and in a pouch. In addition, he gives a quarter talent, roughly 18 pounds, to Lucius Vorenus, again handing it over with little effort, indicating the lack of accuracy.
When Vorneus and Pullo rescue Octavian, he assures them that Caesar will prove his identity. Octavian is eleven-years-old at this point and Caesar was away from in Gaul for nearly eight years, so the last time he would have seen Octavian would have been when he was three. However, upon seeing Octavian Caesar recognizes him straight away.