The red-suited gift-bringer, whose name is Dutch, whose shape is a poem, and whose legend was deliberately built in 1800s New York.
Documented
The paper trail
The name is Dutch Sinterklaas, from Sint Nikolaas, the 4th-century bishop of Myra. First American print mention: Rivington's Gazetteer, 1773, St. A Claus. Washington Irving's 1809 Knickerbocker's History made him a pipe-smoking flying burgher as a joke. The 1823 poem A Visit from St. Nicholas added sleigh, reindeer, and chimney. Thomas Nast's Harper's Weekly cartoons, 1863 to 1886, drifted the coat from tan to red.
Assessment: Documented: every stage survives in print.
Stories
The Coke myth
Everyone knows Coca-Cola invented the red suit. Coke's own history page says otherwise: Santa wore red before illustrator Haddon Sundblom's 1931 campaign, which merely made one plump version inescapable for three decades.
Assessment: Stories: the company that benefits from the myth is the one that debunks it.
Interesting claims
The missing Dutch
The St. Nicholas Center notes historians hunting for Nicholas traditions in colonial New Amsterdam find scant evidence; the Dutch-roots story was largely retrofitted by John Pintard's New-York Historical Society and Irving's satire. Claims of an older Odin-lineage are thinner still.
Assessment: Interesting claims: the origin story of the origin story is itself invented.
Sources and further reading
Rivington's Gazetteer, New York, December 23, 1773: first American print mention, 'St. A Claus'
Charles W. Jones, Saint Nicholas of Myra, Bari, and Manhattan (1978): scant evidence of Nicholas customs in Dutch New Netherland
Washington Irving, Knickerbocker's History of New York (1809): the pipe-smoking flying burgher
'A Visit from St. Nicholas', Troy Sentinel, December 23, 1823: sleigh, reindeer, chimney
The Coca-Cola Company's own history page: Santa wore red before Haddon Sundblom's 1931 campaign
Thomas Nast's Santa cartoons, Harper's Weekly, 1863-1886: the coat drifting tan to red
Worth asking
A real bishop, a satire novel, an anonymous poem, and an ad campaign built the same man; which layer of your childhood was the advertisement?