The traditional Roman male tria nomina were made up of three elements. The tria nomina was a symbol of Roman citizenship and quite often thought as the 'classic' form of Roman nomenclature, but in reality, it was actually used for a relatively short amount of time in Roman history and all sorts of other formulas and variations were popular at different times, but maybe there's no need to go into that just now. Benet Salway's 1994 article offers a classic review of changes in Roman onomastic practise if someone's interested.

We can take Cicero's, that is, Marcus Tullius Cicero's name as an example. There is the praenomen, which was the first name that originally was used as the main diacritic within family (Marcus). Then, there's the nomen gentilicium or sometimes called just nomen (Tullius), which was basically the family name that showed which gens you belonged to. The Romans had laws for protecting these nomina, and using an Italian gentilicium even when you were not a citizen was a punishable offense. The gentilicium always passed from father to sons and daughters, and the praenomen almost always, so that the sons of the family often had the same first name. The last element, the cognomen (Cicero), then was originally used as an added personal touch that could differentiate males in the same family or family line. In reality, these were often hereditary as well, which can make it very difficult to differentiate between generations. Cognomina could for example differentiate between the sons in the family and mark the order of birth; Primus, Secundus, Tertius etc. were very popular. They could also have something to do with the characteristics or achievements of the individual - Plutarch says that Cicero (which means 'chickpea') had gotten his name from an ancestor who had a small nose that looked like a chickpea.

So, to go back to your questions, are you only interested about the praenomina, i.e. the first names? If yes, the Romans had a very limited repertoire of praenomina, some three dozen. Praenomina practically always passed from father to sons, and freedmen usually took their old master's praenomen. So, "what should I call my son?" was very rarely a puzzle for Romans. The Wikipedia article says that about a half of those in the list were in popular use, but I could limit the names that were really popular to an even smaller number; the most common one's you'll see are Gaius, Gnaeus, Lucius, Marcus, Publius, Quintus, Sextus, Tiberius, Titus - perhaps Statius and Servius can make that list as well. Praenomina other than these are pretty rare. I'm pretty sure I've seen statistics for different Roman regions about how popular each praenomen was, but, sorry, I can't remember on my feet where I could find one just now :P There will be regional variations, and I don't think anyone has done a survey for the whole Roman world, since we have tens of thousands of inscriptions and therefore personal names from the Roman era!

If you're interested how common some gentilicia and cognomina are, that's a more difficult question because there are huge amounts of them. Study of Roman personal names, known as onomastics, is a big academic field of its own. People who work on this field, among other things, make lists of gentilicia and cognomina and track how popular certain names are in certain regions and eras. These can be used to make some guesses about where any individual came from the Roman world.