HOW TO CHOOSE A ROMAN NAME
Once you have figured out whether your character will be a roman citizen, a slave, or a former slave (freedman), you can pick out a name using the guide below.
Roman male names typically had three parts (except for slaves and foreigners)
Praenomen - First name
Nomen - Family/Tribe name
Cognomen - Name indicating your particular family line (optional)
You only had a few first names to choose from (because of superstitions regarding names):
Caius or Gaius (the most common), Cnaeus or Gnaeus, Titus, Tiberius, Quintus, Aulus, Decimus, Lucius, Marcus, Postumus, Publius, Quadratus, Sextus, Servius, Spurius, and maybe Primus and Tertius
(Since Servius and Tiberius are names for groups, you will probably want to avoid those).
You can pick your family name from the list of nomina on this page, and add a cognomen (on the same page) if you would like.
You generally took a feminine form of your father's nomen (family name). Find your roman name on this page (the ones with an "f" by them).
Your master gave you a single name. Greek names and names of Roman dieties were popular. (A few slaves also kept the name they had when they were free. Recent slave captures during the time of Nero may have come from Britian or Gaul, so if you want to research and pick one of those names, feel free to check out the "foreigners" section under Celtic or Germanic below to find a name from one of those places).
Upon being freed, a slave took the praenomen (first name) and nomen (family name) of his master, and added what had been his slave name as a cognomen. So, if your character is a praenomen and nomen from this page and pick a slave name using the guide for slaves above.
Freedwomen took the name of their mistress and added their slave name. For your first name find your roman name on this page (the ones with an "f" by them)., and for your second name pick from this list of Greek names or this list of Roman dieties.
Free foreigners only made up about 5% of the Roman populations. If your character was a foreigner, go to these pages to find your name.
A lot of the info here also comes from this site, which talks about naming during the early Imperial era (which is aproximately when our VBS is set in, so was a good source).