The New York is another of the myriad "redowa and mazurka" variations given in M. B. Gilbert's Round Dancing (Portland, Maine, 1890). Along with the Fascination, it is one of only a few variations credited to Indianapolis dancing master D. B. Brenneke. It reappears among the material translated directly from Gilbert in [George] Washington Lopp's La Danse (Paris, 1903), where it is listed as a mazurka and again credited to Brenneke.
Gilbert gives both this "New York" and another dance called "The New York", making it unclear whether the name refers to the city or whether it is simply a new version of the York. Lopp lists it as La New York, along with two different dances called La Nouvelle York. Lopp's translations suggest that the reference is to the city as much as to the popular dance. That might make it something of a pun, since the New York does include the characteristic sliding sequence found in the first measure of the York.
Contradicting this is the appearance of the dance in the addenda of the fifth edition of William B. De Garmo's The Dance of Society (New York, 1892), where it is listed simply as "The York, No. 2", which leads one to the new-version-of-the-York interpretation of the title. De Garmo notes that "This method has become very popular."