Names including Rhiannon, Rhiain, Rhian, Rhianedd, Rhiangar, Rhianwen and Rhianydd all share the Welsh element Rhian-. According to one source (
http://www.medievalscotland.org/problem/names/rhiannon.shtml), Rhian-, derives from British rix "king" and/or from a Welsh word meaning "maiden, virgin".