Not sure precisely why you're being downvoted for bringing some additional light to the conversation. Been busy here but appreciate the insights; this isn't my field. Are there good sources that clarify the complexities of Roman naming conventions?
You're thinking along the lines of generational suffixes? There were Roman emperors who's family name (nomen gentilicium) was a number, the same number being used by son, father, grandfather... not incrementing with each generation.
There were also Roman emperors who's fathers had been slaves.
Lucius Septimius Severus - family name means 7th
Publius Helvius Pertinax - family name means honey-yellow. Son of a freed slave.
"The fifth slave I bought" and "the fifth son of this super rich senator" would have exactly the same name, Quintus.