You cannot do a Constantine movie without the religion part because religion played a massive part in his defeat of Maxentius and would thereafter be instrumentalised in all his campaigns. So unless the movie is Constantine: The Early Years (not an impossibility, he had moer than enough campaigns to justify it) you need to go into the religious aspects of his reign, even if you omit Nicea and the more scholarly parts.
Gaius Julius Caesar was the only person ever to be known as Caesar. Earlier members of his family would have different praenomen since his father was the younger son of a junior branch of a junior branch but in any event his father had he exact same name, as did his grandfather and, possibly, his grand-grandfather. There is no unique name the Caesar we know had but that's no problem because (1) no one cares or has heard about the earlier Julii Caesares and (2) unlike other members of his family, Caesar would be known as Caesar, whereas his ancestors would have been called, in all likelihood, Gaius Julius by their contemporaries. Also, as Teproc mentioned, Caesar would later on become a title instead of a name, but all the emperors were known by their names, from Augustus to Romulus Augustulus.