Because the other reindeer's identities were already established.
The commonly cited names of the reindeer are Dasher and Dancer, Prancer and Vixen, Comet and Cupid, and Donder and Blitzen. They are based on those used in the 1823 poem A Visit from St. Nicholas, arguably the basis of reindeer's popularity as Christmas symbols, where Donder and Blitzen were originally called Dunder and Blixem respectively.
Robert L. May created Rudolph in 1939 as an assignment for Montgomery Ward. The retailer had been buying and giving away coloring books for Christmas every year and it was decided that creating their own book would save money.
So Rudolph having a red nose was just a marketing ploy used by Montgomery Ward.
Yes, Rudolph was unique in having his red nose.
Rudolph the reindeer nose is red
It has never been stated what made Rudolph's nose glow red. Rudolph just happened to be born with a red nose.
Rudolph the Red-Nosed Reindeer's nose was red because he was born that way. It was just something unique about him.
Rudolph The Red Nose Reindeer is 71 years old
Rudolph the red Nose reindeer.
Rudolph the red nosed reindeer
Rudolph's red nose.
Rodolph the red nosed reindeer had a very shiny nose, and if you ever saw it you would even say it glows...
You already have the answer: Rudolph!
Rudolph the red nose reindeer
Donner is Rudolph the Red-Nosed Reindeer's father.