reindeer (n.) Look up reindeer at Dictionary.com
c.1400, from a Scandinavian source such as Old Norse hreindyri "reindeer," from dyr "animal" (see deer) + hreinn, by itself the usual name for the animal, from Proto-Germanic *khrinda- (cognates: Old English hran "reindeer;" German Renn "reindeer," which was altered by folk etymology influence of rennen "to run;" Swedish ren-ko "female reindeer," with ko "cow" (n.)).

Probably from PIE *krei-, from base *ker- (1) "horn, head," with derivatives referring to horned animals (both male and female reindeer have horns; those of the male are remarkable), and thus perhaps cognate with Greek krios "ram" (see kerato-). Older sources connect it to words in Lapp or Finnish. French renne, Spanish reno, Italian renna ultimately are from Germanic.