One s is standard, and it is pronounced as z, as this is the standard English pronunciation of a medial s (as in housed). It may have been used in Wales but it appears to be
Norman, related to French Aslin, a variant of Asceline or Asselin, whose origin is disputed and perhaps represents several older names —
Anselm (
Ans, As- or Os- "diety" + helm "helmet"), Ascelm (Asc- Ash-tree etc.), or from
Asse, Germ. Atzo, a pet form of Adal- (noble, in the sense of having inherited land). An Azelina was the wife of
Richard Tallebois in 1086, and Asselin, Azzelin and Azzelinus are recorded. The Asselin or Alselin who killed
Hereward is a romantic fiction, and the Alselin form a misleading error. The Swedish Surname Aslin is topographical and has no connection.