This name appears briefly in a poem in the Black Book of Carmarthen in the form Kyrridven [1] and in a poem in the Book of Taliesin in the form Kerrituen [2]. Some theories connect her to an otherwise unattested Celtic goddess of inspiration, and suppose her name is related to Welsh cerdd "poetry".
This name was used by Communist parents who were eager to reject traditional names, possibly in the sense of красная заря (krasnaya zarya) meaning "red dawn" (i.e. the dawn of communism). Also note that Zarya was once the name of a Marxist publication as well as of several Soviet scientifically-inclined projects.
Zorya began to be used as a first name during the Soviet era, because a lot of Communist parents were eager to reject traditional names.