I'm not really a Latin speaker, but I have read a good bit about Roman naming practices. From somewhere around the first century BC, Romans tended to use a tripartite naming convention that consisted of a first name, or praenomen, a family name, known as a nomen or gens, and a nickname or cognomen. For example, Gaius Julius Caesar's praenomen was Gaius, his nomen was Julius, and his cognomen was Caesar.
Boys were called by their first names or praenomen up until the time of puberty, when they usually began being addressed by their cognomen. That wasn't a hard and fast rule, however; the first two Flavian emperors Vespasian and Titus, for example, were father and son and had identical names: Titus Flavius Vespasianus. Vespasian went by his cognomen, which was typical, but his son chose to go by Titus, his first name, in order to differentiate himself from his father. And Marc Antony doesn't seem to have had a cognomen at all. So there's precedent, if you're a writer, for making up names that don't necessarily fit the standard.
Now since Marcus and Jasmine were the children of Calphurnus, I would have supposed that that was his cognomen rather than family name since Romans didn't typically refer to men just by their family names. If they were going to include the family name, I believe they would have either added his cognomen onto the end or used his full name. So I don't know that we can be certain what his children's full names were from that.
I'm pretty careful about making up names that fit the culture and period. There are really good articles and lists of Roman names on some of the Roman re-enactment sites. I also have some lists and info on Germanic and Gaulish names from around the first century AD that I use when I need a name for some character of that persuasion.