Gaius Caesar
Since the last Gaius Octavius (Augustus) was adopted by his great-uncle Julius Caesar and became one of the Julii Caesares, the family's original "nomen gentile" was not inherited by his only daughter (i.e. Julia the Elder) and adopted sons (i.e. Gaius Caesar, Lucius Caesar, Tiberius, Agrippa Postumus), which meant the end of the Octavii Rufi's male line.