Likely variant of Anaisa or Anisa, associated with meanings such as "friendly" or "gracious."
Anayssa looks like a creative Arabic-influenced variant that likely grew from names such as Anaisa or Anisa. Those forms are associated with friendliness, grace, and sociability, and Anayssa carries that same gentle semantic field even if its spelling is more modern and ornamental.
The doubled consonants and flowing ending give it a polished, distinctive look. This kind of name shows how traditional sound patterns can be refreshed for contemporary use. Anayssa feels elegant but approachable, with a balance of softness and style that makes it easy to imagine in a wide range of modern communities. It has the advantage of sounding both recognizable and unusual, which is often exactly what parents want from a newer name built on older roots.