The Romans had no formal nomenclature for women beyond the clan name, so when we see Cornelia, or Flavia, or Livia, or Tullia, or Terentia, or Iulia, or Antonia, etc., these forms are simply the feminine forms of the clan names more commonly known by their masculine forms: Cornelius, Flavius, Livius, Tullius, Terentius, Iulius, Antonius, etc.

Many Roman names actually mean something. So, yes, "Flavius" means blond, "Cornelius" is built on the "corn-" root that means horn. Others have no obvious meaning, such as Iulius, etc.

This corresponds to English family names, where some people are named Black, White, Armstrong, Oldfather, Gore, Bush, Thatcher, Smith, Cooper, Numbers, Fisher, Albright, etc., while many others are meaningless in English, such as Eisenhower, Blair, Jones, James, Fitzgerald, Reagan, Liebermann, Cheney, Gere, etc.