Both the name Rudolph and his red nose are artistic choices made by the character's creator, Robert L. May. May created the character and associated story in 1939, for a promotional coloring book distributed by Montgomery Ward. According to Wikipedia Red-Nosed Reindeer - Wikipedia, the free encyclopedia:
Of note is the change in the cultural significance of a red nose. In popular culture, a bright red nose was then closely associated with chronic alcoholism and drunkards, and so the story idea was initially rejected. May asked his illustrator friend at Wards, Denver Gillen, to draw "cute reindeer", using zoo deer as models. The alert, bouncy character Gillen developed convinced management to support the idea.
Though the truth goes no deeper than that, others (including respected scientists) have opined on the subject, e.g.: