Asterope is the name of several characters from Greek mythology. Among them is a Naiad who died fleeing prince Aesacus (although her name is more reminiscent of a star-nymph than a Naiad, so perhaps she was envisioned as a shooting star, dying upon the Earth). Asterope is also an alternative name for the Pleiad Sterope and the Hesperid Hesperia.
A famous bearer was the Italian racecar driver and industrialist Enzo Ferrari (1898-1988).
As an English name it was not used until after the Protestant Reformation. It was utilized by George Eliot for the title character in her novel Silas Marner (1861).