Annis \a(n)-nis\ as a girl's name is pronounced a-NISS. It is of Greek origin, and the meaning of Annis is "satisfaction". May also have developed in the Middle Ages as a mainly Scottish form of Agnes, which means "holy" in Greek. Anysia is the name of a fourth-century Thessalonian saint. See also variants of Ann.
For more information, see also the related name Anice.