What did Caesar mean before Caesar was Caesar?

https://i.imgur.com/vw4c3ry.jpg

There were conflicting etymologies in antiquity for the cognomen of the Caesar branch of the gens Julia, and to my knowledge the etymology is still disputed. The two most common(at least now) etymologies are Pliny's and Festus'. Pliny said it came from the verb caedo, to cut, as he says that the first member of that branch of the gens was born a caeso matris utero, "from his mother's cut womb." An alternate (if modern) possibility is that, if Caesar derives from caedo, it was not because the individual was cut from the womb, but rather that he did the cutting, as a surgeon or a butcher or something. I cannot comment on the linguistic plausibility of that suggestion. Servius and Nonius both prefer this etymology. Festus offered the etymology that it was from caesaries, "a head of hair" (a caesarie dictus, qui scilicet cum caesarie natus est, "he was named from his hair, since of course he was born with a full head of hair"). This etymology seems strained, although it was popular in the early twentieth century (Robert Graves used it in I, Claudius, for example). One of the authors of the Historia Augusta includes a lengthy passage about possible etymologies of Caesar, mentioning among others both previous etymologies. One possibility he mentions is from caesius, "grey (or blue)", quod oculis caesiis et ultra humanum morem viguerit, "since he [the ancestral first holder of the cognomen] had blue eyes and was lively beyond human custom [in reference to the use of caesius to describe divine eyes]." The same author also suggests an etymology from caesai, which he says is the Mauretanian word for elephant: ab elephanto, qui lingua Maurorum caesai dicitur, in proelio caeso, "on account of an elephant, which in the Mauretanian language is called caesai, that he slew in battle." This last etymology was favored by the Caesars themselves, at least during the lifetime of Gaius Caesar, who issued denarii in 49 with the image of an elephant and the inscription "CAESAR." But as is so common with these extremely ancient cognomina (although the Caesars only appear as a branch in 170, during Sex. Caesar's legateship) the etymology is uncertain. Compare Kaeso, also said by Pliny to be from caedo for the same reason, but which Mommsen argued was descended from caedo not because of cutting the mother's womb but because the gentes Fabia et Quinctia, which held the cognomen, were involved early on in the Lupercalia and the ritual striking (an alternate meaning of caedo) of the city's women as part of a fertility rite.