"I come to bury Julius, not to praise him?"
Sorry, but it's just not right
So while you may be right, that doesn't seem like the strongest argument.
Same goes with Cicero, for example, his given name was Marcus and he was form the Tullian family, but the name we know him by and the romans did too is Cicero, which comes from very remarkable dimples he had, and so he called him Cicero, which can be translated as chick-pea.
Going back to Caesar, the case is a little bit different because his name was indeed also inherited by his father, whose name was also Gaius Iulius Caesar. Historians argue about the origin of the name Caesar, and we can't be sure, but it definitely was not a title during his lifetime.
Calling him Julius is like referring to Elizabeth II as Windsor.
I know like dozens of Adrian, Adrià, Adrianne, Ariadne, etc.
That H is just Evil