Would it better if the name was New York City?
I found in the history of the relation that the name and the alt_name were flipped (name from New York City to New York and opposite for alt_name) in version 75, that was included in a changeset without comment (https://www.openstreetmap.org/changeset/71280084) by user Антін Сартенченко published 06/15/2019.
Was this changeset tacitly accepted by the New York community?