[q_an_a]

There was a PBS "history detective show" that tracked this work to another man, don't know the name, who Mr. Moore copied in another work. This person was a signer of the Declaration of Independence and gave the oath of office to Washington. The original author knew German for which the reindeer's names are derived and Mr. Moore had no such knowledge. The list went on and on.

[Oztrich Boy]

There was a PBS "history detective show" that tracked this work to another man,

Major Henry Livingston

The matter is confused by the fact there were two Santa Claus poems in the 1820s.
The probable Moore Old Santeclaus (1821) and A Visit from St Nicholas (1823).

The latter was more popular than the mean-spirited Old Santeclaus and with Livingstone dead c.1830, the authorship was assigned by rumour to the more prominent Moore.
Moore chose not to dispute this and later included VFSN in a book of Christmas poetry without actually claimng he wrote it.