Surnames also started as nicknames! And for the same reason: to differentiate between people in the same community with the same given names.
However, there is so much that we don't know about Roman naming practices for women that it's very hard to say a sensible word about it. The point you are making is a valid one, though: Aquilius Severus very easily becomes Aquilia Severa, just as, say, bonus deus can become bona dea. And it could clearly help in identifying her more accurately. But both Caesar and Nero are third declension nouns, and therefore would look the same in masculine and feminine forms, where these exist or could exist. If you put a clearly feminine adjective, or of course given name, a first declension one, next to one of these third declension cognomina, you could theoretically use it to refer to a female Caesar or Nero: but your female Caesar would be Julia, say, already so there wouldn't really be much point in calling her Julia Caesar.