I would presume that Caspian is his first name. As for his last name, it would probably come from the name of his House/Dynasty. Megas Alexandros was of the Argeads (my House), which derived from the name of a mythical ancestor, Argos (I think that he was supposed to be the Argonauts shipbuilder, but he could have been the founding king of the city of Argos). Unless Caspian had someother mythical ancestor, besides his forebear Caspian the Conqueror, I can't see where a surname would derive from. Perhaps, assuming there is a seperate and independent Telmarine language, the word for conqueror, victorious warrior, or saviour (similar to Soter, Bhadur, or Khan) could serve as a surname (name of his royal House). But none is given, at least specifically. So, I geuss we're left to speculate.
See ya on the flipside,
Cyon Corell