Nothing to do with Bed-Stuy, which is in Brooklyn.
Peter Stuyvesant was the last Dutch Governor of New York, so the name is common throughout the city.
Stuyvesant High School is in Manhattan ... originally on 15th St. and 1st Ave when I went there, now on Chambers St near the WTC.
I’ve never been to NYC so I was under the assumption the school was in Bed-Stuy.
From what I understand, Peter Stuyvesant wasn’t such a great guy.