This is Phil "Scooter" Rizzuto Park, renamed in 2008 for the late, great Yankee shortstop, who played baseball at nearby Richmond Hill High School. (Other notable alumni of the school: Cyndi Lauper, who attended for a while before being expelled, and Rodney Dangerfield.) The park's former name was Smokey Oval, which "refer[red] to the park’s location, across from a Long Island Railroad terminus which once made it a landing area of soot and ash from the railway smoke", according to the Parks Department.
The NY Times reported that the area's sizable Sikh population was in favor of changing the park's name, given the religion's prohibition against smoking. As a co-founder of one of the local Sikh temples explained to the paper: "It sounds like a place for smoking and drinking and things like that . . . When we print up fliers, we have to say we are having an activity in nearby Smokey Park."
UPDATE: It turns out that this park has for decades been the center of bird song "racing" in New York. The races, which take place on Sundays, are competitions between two bird owners, typically immigrants from Guyana and other Caribbean and South American countries, to see whose chestnut-bellied seed finch (like the one pictured above) can sing 50 songs first. You can read more about the birds and the men behind them here.