Of uncertain origin. If not simply an invention, it may have been devised as a feminine equivalent of Alan (of which it is an anagram), or a shortened form of Alana. It seems to have been first used by the American film actress Lana Turner (1920–1995), whose original name was Julia.
English and German: classicized spelling of Randolf, a Germanic personal name composed of the elements rand ‘rim’ (of a shield), ‘shield’ + wolf ‘wolf’. This was introduced into England by Scandinavian settlers in the Old Norse form Rannúlfr, and was reinforced after the Norman Conquest by the Norman form Randolf.