Interesting that Roman women did not acquire names (as opposed to "the big daughter from the Balbus branch of the Atius clan who is married to one of the Marcii") until the very end of the Republic:
Roman Nomenclature: [F]emale children of citizen families were named with the feminine form of the clan into which they were born; hence, all women whose fathers had the nomen Julius were named Julia, and all women whose fathers had the nomen Cornelius were named Cornelia. In public, they would be identified by the possessive form of their father's cognomen (e.g., Julia Caesaris, “Julia, the daughter of Caesar”), or if married by the possessive form of their husband's cognomen (e.g., Clodia Metelli, “Clodia, the wife of Metellus”). If families had more than one daughter, they were distinguished by the words maior and minor (“elder” and “younger”), or prima, secunda, tertia, etc.
However, by the late Republic these conventions were changing slightly, in that elite Roman woman were sometimes designated by the feminine form of their father's nomen plus the feminine form of his cognomen, sometimes in the dominutive (e.g. Livia, who married Octavian and became Rome's first empress, was often referred to as Livia Drusilla, since her father was a noble named Marcus Livius Drusus). Starting with Augustus, names of the most prominent women did not necessarily follow the Republican convention, but rather reflected the family connections that were most significant to the namers. For example, the two daughters of Augustus' daughter Julia, who was married to Marcus Vipsanius Agrippa, would normally have been named Vipsania; instead one was called Julia and the other Agrippina. When Agrippina married Nero Claudius Germanicus (grandson of Livia), her three daughters were named Agrippina, Drusilla, and Julia Livilla (referring to the family lines of both of their distinguished great-grandparents) instead of Claudia, which would refer to their father's nomen.
So why, in "Rome," is Atia called "Atia Julii" rather than the proper "Atia Balba Marcii" (after her second husband Lucius Marcius Philippus)? Presumably for the same reason that Pompey and Caesar are called "co-consuls" rather than proconsuls. The consuls for the years 50 and 49 were L. Aemilius Lepidus Paullus, C. Claudius Marcellus, and L. Cornelius Lentulus Crus...