This appears to have begun in Chicago, not New York. The term is of historical interest today.
12 November 1930, New York Times, pg. 12:
CHICAGO, Nov. 11. - Hooverville, so-called by a colony of unemployed men, has sprung up in Chicago's front yard at the foot of Randolph Street near Grant Park, like one of the mushroom mining towns of bonanza days of the Far West.
16 November 1930, Los Angeles Times, pg. A7:
Shack Settlement Boasts
Name of "Hooverville"