Alot of old Tottenham, which part of Harringay was in, grew up around greens; hence Wood Green, West Green, Palmers Green, etc. Harringay was Beanes Green. We still could be, but for Harringay House. See the attached 17th Century map fragment - oddly it was drawn with South to the top of the page. The big road on the right is Green Lanes (You get where its name came from now).
Hangers Green, on Hanger Lane, (now St Ann's Road) is at the junction of what's now Blackboy Lane and St Ann's Road.