Santa Claus’ reindeer first appeared in an 1823 poem A Visit from St. Nicholas (a.k.a. The Night Before Christmas or ‘Twas The Night Before Christmas) by Clement Clark Moore. In it, they were named Dasher and Dancer, Prancer and Vixen, Comet and Cupid, and Dunder and Blixem.
Dunder and Blixem were never part of the poem I learned; they were chosen because they translate to Thunder and Lightning in Dutch. However, the poem was later adopted to use the German usages, Donner and Blitzen.