Lucania is a fun way to get Luca as a nickname for a girl, without having to use Luca alone, since Luca is an Italian boys name. Like Atticus, Lucania is a place name, the ancient district in southern Italy, which spread from the Tyrrhenian Sea to the Gulf of Taranto. Today the modern region is known as Basilicata. Since changing the region's name, Lucania can be found as a surname as well. There are only a handful of place names that are no longer places, such as Abyssinia and Anatolia, and if we're talking rare (which we're always talking about on this blog) these names have you covered - rarity, history, and beauty.
Lucania is derived from one of two sources: either the Greek leukos, meaning "white," from lux, or the more likely source of the Latin word lucus, meaning "Sacred Wood," but also from the root of the Latin word lux, meaning "light." The meaning "chaste light" or "sacred light" can also be given. It does not mean "mother of Rome," as other sites would have you believe. It is important to note that the boys names Loukas, Lukas, Luke, and Lucan come from the same origin, so if you'd rather see Luca on a girl, Lucania is the way to go. Lucasta is the more widely known English female name with the same meaning.
There have been no babies named Lucania in the U.S. in quite some time, but approximately 4 women have this as a first name, and 189 people have it as a surname.