Of uncertain derivation. Stacey and Stace are recorded as given names in the Middle Ages, probably pet forms of Eustace. The medieval name seems to have fallen out of use by the 16th century, and the modern given name is probably a transferred use of the surname, which is likewise derived from Eustace. It is not clear why this name should have become so common in the 1970s and 80s as a girl's name (less commonly as a boy's name).
Italian and Jewish (from Italy): habitational name from the Sicilian city of Palermo, the Greek name of which is Panormos, from pan ‘all’ + ormos ‘gulf’, ‘bay’, probably in the sense ‘wide gulf’, but possibly ‘well-protected bay’.