Local History Nerd here to help you with your struggle. Your choice would depend entirely on which kind of Roman Theme you’re going for. Caesar/Imperator was the title for the ruler of the West and East each. Sometime after the West fell (and we started knowing the east as byzantine) the title changed to Basileus/Basileos, Caesar at that point was a title given to a close relative of the Emperor.
In short Basileos if you’re going for late Rome, as Caesar would be just an honorary title.
Imperator/Caesar if you’re going for regular roman inspiration.
Alternatively “Augustus” could be used, as its a title rather than a name, it means “First Citizen”.