Tens toda a razão, e a palavra Knick (diminuitivo de Knickerbocker) tem uma origem engraçada e uma relação interessante com a cidade:
"The most interesting question in basketball at this moment, lexicographically speaking, has to do with the New York Knickerbockers. (Sorry, LeBron James.) Now, before you start throwing knickknacks at your computer screen, indulge a brief explanation.
Knickerbocker was a common surname among the Dutch colonists of New York way back when it was New Amsterdam. The wonderful early American writer Washington Irving famously used it as a pseudonym in his History of New York, and Knickerbocker has since been another way of describing a New Yorker. So, unlike some sport team names which make no sense, the Knicks is rich with Big Apple history."