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Its derived from his family. The Julii were one of the oldest families of Rome, traditionally having been Alban in origin and joining the city after Tulus Hostillius brought about the subjugation and then destruction of Alba Longa.

The name itself is a traditional name of one of the sons of Aeneas, the "founder" of the Roman people when his Trojan band finally settled amongst the Latins.

The Caesar branch was then a branch of the Julii family, with Gaius Julius Caesar being the most prominent member. But female family members generally just took the feminine forms of their father's name, so there were MANY Julia's, and Claudia's, Flavia's.

There had been many Julia's before then, one Julia Caesaris in particular was his Aunt and the wife of Marius the Roman general and statesman. When she died he is reported to have given a memorable funeral oration. The way it has come down to us helps inform how much weight the Romans placed on family history and bloodlines.

"The family of my aunt Julia is descended by her mother from the kings and on her father's side is akin to the immortal gods. For the Marcii Reges go back to Ancus Marcius, and the Iulii, the family of which ours is a branch, to Venus. Our stock therefore has at once the sanctity of kings, whose power is supreme among mortal men, and the claim to reverence which attaches to the gods, who hold sway over kings themselves."