Yaiza is a name from Guanche origin (the Guanches were the old inhabitants of the Canary Islands). It is a place name which has been used as first name in last years, mainly because of a trilogy by Alberto Vázquez Figueroa.
The place name Yaiza means "one that shares" or "one that divides in two identical halves", according the studies in Guanche onomastics and linguistics.
"-Yaiza (TIT) (tomado del término municipal correspondiente, antiguo nombre maho) ("la que comparte" "la que divide en dos partes iguales")"http://elguanche.net/antroponimosgt.htm
The meaning "rainbow" or "rainbow princess" appears in non-reliable names webs and books. Probably, this meaning comes from the story in Vázquez Figueroa's books and from some other stories in recent books with characters named Yaiza.