The Roman province created from Ptolemaic Egypt after Octavian’s annexation was called Aegyptus. Octavian established it after conquering Alexandria in 30 BC and ending the rule of Cleopatra VII and the Ptolemaic dynasty.
Aegyptus was unusual among Roman provinces. Because Egypt was exceptionally wealthy and strategically important, the emperor kept unusually tight control over it. The province was generally governed by a prefect from the equestrian order rather than a senator, and senators required imperial permission to enter.
Egypt supplied Rome with enormous quantities of grain, especially for the population of Rome. Alexandria remained a major administrative, commercial, and intellectual centre, while traditional Egyptian religious and bureaucratic institutions continued under Roman supervision.
Aegyptus should not be confused with Judaea, Cyrenaica, or Africa. Those were separate Roman territories. The name also reflects Roman administrative usage; Egypt remained culturally Egyptian and Greek-speaking in many settings even after annexation.