Later it was used by Giovanni Pacini in his work "Amazilia" (1826), where it belongs to a young Indian woman, and the scene takes place in Florida. Looks like he borrowed this unsual name from the novel of Marmontel. The daughter of the composer was also named Amazilia. She is depicted on famous painting "Horsewoman" (1832) by Karl Bryullov.
In Georgia, this name is a diminutive of Valentina and Valerian, though there can certainly be cases where it is the georgianized form of the aforementioned Valya. In this day and age, Valia is primarily used on women in Georgia.
In Greece, this name is strictly feminine and is a pet form of Vasilia and Vasiliki.
Known bearers of this name include the Georgian revolutionary Valerian "Valia" Bakhtadze (1896-1930) and the Greek model Valia Kakouti (b. 1981).