Many had a third name, the cognomen (additional name, nickname;
often denoted a branch of a family).
The cognomen originally showed a peculiarity personal to one individual, e.g., Scaevola ("Lefty"), Balbus ("Lisper"), Cursor ("Runner", perhaps "Speedy"). An inherited cognomen, however, did not indicate a personal characteristic other than descent from the original holder of the name.
A second cognomen (or agnomen) could be added to show an achievement: P. Cornelius Scipio Africanus (conqueror of Africa).
A person adopted into another gens could also be identified by an adjectival name indicating his family of birth:
P. Cornelius Scipio Aemilianus, the son of L. Aemilius Paullus; Scipio Aemilianus was born an Aemilius.
Some families were so large (and so often favored the same praenomen)
that most men in the family soon acquired nicknames in order to be distinguished
from each other, for example, the Metelli, many of whom [or at least many
of those encountered in a history textbook] were named Q. Caecilius Metellus.
But they are easy to tell apart when called by their last two names:
Metellus Numidicus = Q. Caecilius Metellus Numidicus (fought successfully in Numidia) and his son
Metellus Pius = Q. Caecilius Metellus Pius (so-called for his devotion to his father's rights)
There were few individual first names in common use; these were abbreviated on inscriptions and in documents. When pronouncing these names, it is proper to say the whole name, not the initial.
Ap. (App.) Appius