Life Of Siberian Reindeer Herders, Yamal, Russia.

The name rangifer, which Linnaeus chose as the name for the reindeer genus, was used by Albertus Magnus in his De animalibus, fol. Liber 22, Cap. 268: "Dicitur Rangyfer quasi ramifer". This word may go back to a Saami word raingo. For the origin of the word tarandus, which Linnaeus chose as the species epithet, he made reference to Ulisse Aldrovandi's Quadrupedum omnium bisulcorum historia fol. 859—863, Cap. 30: De Tarando (1621). However, Aldrovandi - and before him Konrad Gesner - thought that rangifer and tarandus were two separate animals. In any case, the tarandos name goes back to Aristotle and Theophrastus.
Local names
The name rein (-deer) is of Norse origin (Old Norse hreinn, which again goes back to Proto-Germanic *hraina and Proto-Indo-European *kroino meaning "horned animal"). In the Finno-Permic languages, Sami poatsu (in Northern Sami boazu, in Lule Sami boatsoj, in Pite Sami båtsoj, in Southern Sami bovtse), Mari pučə and Udmurt pudžej, all referring to domesticated reindeer, go back to *počaw, an Iranian loanword deriving from Proto-Indo-European *peḱu-, meaning "cattle". The Finnish name poro may also stem from the same. The name caribou comes, through French, from Mi'kmaq qalipu, meaning "snow shoveler", referring to its habit of pawing through the snow for food. In Inuktitut, the caribou is known by the name tuttuk (Labrador dialect). In Cree-Montagnais-Naskapi dialects the caribou is called atihkw.