Short answers, pulled from the story.
During the Roman Republic, the essential elements were simply the praenomen and nomen while cognomina appeared first among aristocrats around the second century BC. Plebeians rarely adopted surnames until much later making the three-name structure uncommon for most citizens.
Most women came to be known simply by their nomen sometimes combined with a cognomen if distinction was needed among sisters. When multiple daughters existed in one household they received ordinal identifiers like Servilia Major or Servilia Minor instead of traditional first names.
The edict issued by Emperor Caracalla in AD 212 granted citizenship to every free man within the empire fundamentally altering the naming landscape. These newly enfranchised citizens automatically adopted the name Marcus Aurelius rendering the praenomen and nomen useless as unique identifiers.
By the third century AD the cognomen had become the most important distinguishing element often serving as the sole practical identifier for individuals within large families. This proliferation meant that by the third century bearing several cognomina was the norm rather than the exception for Roman men.
By the fifth century AD the complex Roman naming system began to disintegrate alongside the collapse of central authority in the west. Praenomina became so rare in written records that only the oldest aristocratic families continued to use them into the sixth century.