Annys \a-nn-ys\ as a girl's name is a variant of Anice (Greek) and Annis (Greek), and the meaning of Annys is "satisfaction".
The baby name Annys sounds like Annus and Annes. Other similar baby names are Anny, Agnes, Annise, Annisa, Annest, Annais, Anis, Anais, Agnus, Alys, Allys, Anayas, Anya, Anna, Andy, Angy, Aniya, Ann, Anyu, Annie, Anni, Anne, Annet, Annah, Annwyl, Annot, Anwyn, Denys, Ennis, Innis, Annda and Innes.