Julius Caesar is supposed to have gone bald early. I recall a line from I Claudius supposedly from one of his older veterans about "locking up your sons and daughters, here comes the bald headed whoremonger!".
Pruitt
Indeed, but that does not necessarily rule out caesaries (mane of hair) as the origin.
While a cognomen was a bit like a modern nickname in that people often ended up with one that described some physical trait, they were unlike modern nicknames in that they could be passed onto descendants whether or not they shared the same physical trait.
Who your ancestors were was very important to the ancient Romans, particularly for the Senatorial class, who made the most of having a distinguished lineage to get elected. To the Roman mind, these people inherited the traits of their ancestors. The cognomen Caesar was carried forward in part because it advertised to all that Gaius Julius (and his father before him) was a descendant of Sextus Julius who was elected Praetor in 208 B.C. and commanded troops in the Second Punic War.
Whatever the meaning of Caesar, it was given to Sextus and all descendants inherited the cognomen due to their familial connection to Sextus. Assuming for a moment that the origin was "mane of hair," it may be that unlike Gaius Julius Sextus had a full mane of hair. Or he might have been just as bald and the cognomen was an ironic bit of humor at his expense. Some cognomen poked fun at the people they were originally applied to, and they were passed onto descendants with no less frequency.