Apparently from the name of the River Rhine in western Germany, which is ultimately from Gaulish Renos meaning "that which flows". It was used by American author Lauren DeStefano in her 'Chemical Garden Trilogy'.
From Middle English Rine, Ryne, from Old English Rīn (“the Rhine”), from Middle High German, ultimately Proto-Germanic *Rīnaz, from Gaulish Rēnos, from a Pre-Celtic or Proto-Celtic *Reinos; one of a class of river names built from Proto-Indo-European *h₃reyH- (“to move, flow, run”).