The Oxford Names Companion, OUP "Scottish Forenames" - Donald Whyte, FGH, FSG
Notes:
Scottish and English; originally the Anglicized form of the Scottish Gaelic name Ruadh "red", i.e. "red-haired". The derivation from the French word roi, "king", came later.
Thanks to Donald Whyte who provided much of the initial information for this site.