[Suppafly]

Another less popular theory is that it's from caesus which means to cut, which would be interesting because the cesarean section, also known as a C-section, was named after Caesar so it'd be a bit of circular definition.

>because Gaius Julius or one of his ancestors

Sextus Julius Caesar is the first Julii Caesares according to wikipedia. I just love that the term for all of them is Julii Caesares.