I'm trying to describe the crazy naming conventions for the Imperial Family that I lifted (and simplified) from Roman history. Following is the tentative description to tack on to the end of the Galactipedia - Rise of the Julii article. It comes immediately before the chapter where the reader first meets the Imperator and Imperatrix. Is it intelligible?
Although naming conventions used by the Imperial Family have varied greatly over two thousand years, they currently follow a comparatively simple format: title praenomen nomen cognomen1 [cognomen2] suffix.
title is one of Imperator for the emperor, Imperatrix for the empress, or Heres Imperialis for the Imperial heir. praenomen is the first or given name. nomen is the family name and has remained Julius since the founding of the Imperium. cognomina are further honorifics for the titled individuals. Individuals are usually addressed by their cognomina rather than by title.
For example, the current heir is Heres Imperialis Apollo Julius Caesar III. Apollo is his given name and Julius his family name. Caesar is an honorific bestowed upon the Heres Imperialis at birth (or upon adoption, when there is no natural male heir). Apollo is addressed by his given name by those close to him. Otherwise, he is addressed as Caesar. He is the third Imperial heir named Apollo.
When the Heres Imperialis takes the throne, he adds Augustus as a second cognomen and is addressed as such. The current emperor is Imperator Nero Julius Caesar Augustus V. His given name is Nero, but he is usually addressed as Augustus, even by his sons.
The current empress is Imperatrix Elizabeth Julius Augusta, and she is addressed as Augusta.