Alyss is not commonly used as a baby girl name. It is not in the top 1000 names. In 2012, out of the family of girl names directly related to Alyss, Alice was the most popular.
Baby names that sound like Alyss include Alleece, Aalish (Gaelic), Aaltje (Dutch, Frisian, and German), Ajla (Slavic), Alaxis, Alcee (English), Alcie (English), Aleks (Russian), Ales (Czech), Alex (English), Alexes, Alice (Czech, English, French, Italian, German, Portuguese, and Scandinavian), Alique, Alis (Armenian, English, and Welsh), Alishay, Alisse, Alisz (Hungarian), Alix (English, Greek, and French), Aliz (Greek and Hungarian), and Alize (English, German, and Greek).
† approx English pronunciation for Alyss: AE as in "at (AE.T)" ; L as in "lay (L.EY)" ; IY as in "eat (IY.T)" ; S as in "see (S.IY)"