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[Sebastianus]

I know it's too late but here's a translation from "De Cerimooniis" on an imperial coronation in the 10th century Roman Empire.

 

Imperial Coronation

 

I was thinking, you might give your son the title "born in purple" (Porphyrogennetos) below is an excerpt from the Wikipedia article about Constantine VII.

 

"His nickname alludes to the Purple Room of the imperial palace, decorated with the stone porphyry, where legitimate children of reigning emperors were normally born. Constantine was also born in this room, although his mother Zoe had not been married to Leo at that time. Nevertheless, the epithet allowed him to underline his position as the legitimized son, as opposed to all others who claimed the throne during his lifetime. Sons born to a reigning Emperor held precedence in the Byzantine line of succession over elder sons not born "in the purple"."

 

Wikipedia Constantine VII Porhyrogennetos

 

The title Caesar was used for an heir apparent until the Komnenoi introduced Sebastokrator in the 11th century, then later Despot replaced Sebastokrator. Usually though, the emperors who wished to designate an heir raised them to co-emperors.