"Rian" is also a (somewhat uncommon) nickname for the Welsh name Arianwen. It's typically pronounced as one syllable "REan" (unlike Arianwen, which has a break "ari-YAN-wen").
The name Rian comes from the Galic and is the original spelling of Ryan. Rian is beleived to be the male version of Rhianon. The link is deep in Celtic mythology.
Rian is a character in Marion Zimmer Bradley's "Avalon" series. She is High Priestess of Avalon, mother of Saint Helena, grandmother of Constantine the Great.