The reindeer in "Rudolph the Red-Nosed Reindeer" have the following names:
Rudolph - the reindeer with the shiny, glowing red nose
Clarice - Rudolph's love interest
Dasher, Dancer, Prancer, Vixen, Comet, Cupid, Donner, and Blitzen - the eight other reindeer who pull Santa's sleigh
Hermey - the elf who wants to be a dentist
Burl Ives - the snowman who narrates the story
There are also other characters in the story, such as Yukon Cornelius and the Island