If memory serves Roman women did not have the traditional 3-name structure as men with a praenomen, nomen, and cognomen (eg. Gaius Julius Caesar). They were typically given a femine variant of the family name (nomen). Julia, in the case of of the gens Julius. Sisters were often differentiated with the terms major or minor following the family name (Julia Major), but I believe the descriptive nicknames you mentioned could also serve this purpose. They certainly had family names though. The following is an excerpt from http://www.forumromanum.org/life/johnston_2.html#58

Names of Women. No very satisfactory account of the names of women can be given, because it is impossible to discover any system in the choice and arrangement of those that have come down to us. It may be said that the three­fold name for women was unknown in the best days of the Republic; praenōmina for women were rare and when used were not abbreviated. More common were the adjectives Maxima and Minor, and the numerals Secunda and Tertia, but these, unlike the corresponding names of men (§ 44), seem always to have denoted the place of the bearer among a group of sisters. It was more usual for the unmarried woman to be called by her father’s nōmen in its feminine form, with the addition of her father’s cognōmen in the genitive case, followed later by the letter f (fīlia) to mark the relationship. An example is Caecilia Metellī. Caesar’s daughter was called Iūlia, Cicero’s Tullia. Sometimes a woman used her mother’s nōmen after her father’s. The married woman, if she passed into her husband’s “hand” (manus, § 23) by the ancient patrician ceremony, originally took his nōmen, just as an adopted son took the name of the family into which he passed, but it cannot be shown that the rule was universally or even usually observed. Under the later forms of marriage the wife retained her maiden name. In the time of the Empire we find the threefold name for women in general use, with the same riotous confusion in selection and arrangement as prevailed in the case of the names of men at the same time.

Hope this helps. If someone has a better source on hand go for it.