Santa Claus’s sleigh-pulling reindeer with a red nose is Rudolph.
Rudolph is a fictional reindeer created by Robert L. May in 1939 for a Christmas booklet distributed by Montgomery Ward. In the story, Rudolph is mocked because of his unusual luminous red nose, but his distinctive feature becomes valuable when fog threatens to obscure Santa’s route. Santa asks Rudolph to lead the team, turning the supposed defect into a heroic strength.
The familiar character was added to the traditional team of eight reindeer named in the poem “A Visit from St. Nicholas.” That makes Rudolph commonly known as the ninth reindeer, although the original poem did not include him. His fame expanded through Johnny Marks’s 1949 song, recorded successfully by Gene Autry, and the 1964 stop-motion television special.
A common mix-up is treating Rudolph as one of the original eight or confusing the character with a generic reindeer name such as Dasher, Comet, or Blitzen. Those names belong to the older team; Rudolph is the later red-nosed addition.