I had always heard that Roman names like Septimius and Octavia were given based on birth order within the family but this piece suggests it was more likely the number of the month of their birth:
There’s a Balinese tradition similar to this, where they have a few name options for each child in order up to the 4th child. If you have 5 or more children you start again from the first name and append “balik” which basically translates to “return to” or “again”.
https://latin.stackexchange.com/questions/15623/why-did-so-m...