Unice is girl's name of Greek origin. It is a variant of Eunice, which means "good victory." Perfect for little girls with big and charismatic personalities, Unice is a lovely name brimming with old-school charm and vintage vibes. Wherever life takes you, with baby Unice by your side, you will feel like winning every day. Famous people with this name include Eunice Kennedy Shriver, an American philanthropist and the sister of former US president John F. Kennedy.