I was curious as to why some Romans only had two names. I found out that during the empire the praenomen's function was gradually eroded and no longer recorded, but I could not find anything on the Republic times.

Why did some people, like Marcus Antonius, Gaius Marius, Gnaeus Pompeius, only have 2 names, while people, like Caesar, had 3 in same time period? Did they only have praenomen and nomen or no praenomen with a nomen and cognomen?

thanks,