The character of Rudolph the Red-Nosed Reindeer is not in the public domain. However, he has been popularly (and, more importantly, generically) referred to as "Santa's 9th Reindeer."
* Little Tooktoo, by Marie Ahnighito Peary (1930)
*Rudolph the Red-Nosed Reindeer was created in 1939 by Robert L. May and his first appearance was renewed in its 28th year, meaning the name "Rudolph the Red-Nosed Reindeer" cannot be used without permission. However, an unnamed reindeer with a red nose (or a reindeer with a red nose and a different name) can appear in other works.
**Technically, no one can own the name "Rudolph" so, without it being followed by "the Red-Nosed Reindeer" (again: ''technically''), one couldn't be sued (but, it would be risky).
*The earliest mention of the term "Santa's 9th Reindeer" (when referring to Rudolph) is in the 1964 special, ''Rudolph the Red-Nosed Reindeer'' (where the profile picture was taken from). The copyright year in Roman numerals was mis-marked as MCLXIV (1164) instead of the correct MCMLXIV (1964). Per U.S. law at the time, this invalidated the copyright, causing it to enter the public domain immediately upon release. It did not, however, invalidate the trademark on the name, which is still owned by The Rudolph Company.
*[https://www.amazon.com/Santas-9th-Reindeer/dp/B00PT613GK Amazon]
*[https://archive.org/details/SantasNinthReindeer archive.org]
*[http://www.answers.com/Q/Name_Santa's_ninth_reindeer?#slide=1 answers.com]
*Myths in Media Wiki
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1964 (sort of... see "Notes" section)
The character of Rudolph the Red-Nosed Reindeer is not in the public domain. However, he has been popularly (and, more importantly, generically) referred to as "Santa's 9th Reindeer."
Robert L. May & Romeo Muller (sort of... see "Notes" section)