It is the etymology everyone reaches for. The caesarean section is named after Julius Caesar, who was supposedly cut from his mother's womb, which is also why we say a baby is 'delivered by C-section'. Two facts for the price of one, and they prop each other up so neatly that nobody stops to poke at them.
Caesar's mother, Aurelia Cotta, lived for decades after his birth and is recorded advising him as an adult. In the Roman era, cutting a baby from the womb was something done when the mother was already dead or dying, because she had essentially no chance of surviving it. So Caesar almost certainly was not born this way. The naming is likely a coincidence or a later legend. The word probably comes from the Latin verb 'caedere', to cut, the same root as 'incision' and 'concise', and Roman law that required such a procedure was called 'lex caesarea'. The Caesar connection got bolted on afterwards because it makes a better story. Two famous facts, both wrong, holding hands.