Chasta \ch(as)-ta\ as a girl's name is a variant of Chastity (Latin), and the meaning of Chasta is "pure".
The baby name Chasta sounds like Chasty and Shasta. Other similar baby names are Chanta, Chanda, Chante, Chantay, Chantae, Chaunta, Chantea, Chantai, Charista, Charita, Charty, Chasina, Chasity, Chassy, Chasiti, Chastina, Chastin, Chastady, Chasida, Chasaty, Chesea, Chessa, Chesna, Christa, Chrysta, Chita, Shanta, Shastah and Shahsta.