As Caressa says, Pessy is a Yiddish form of
Basia. (The second Hebrew version.)
I would bet that most of these girls have been born to Orthodox or Hasidic Jewish families in New
York. They are probably going to be living in neighborhoods where everyone is familiar with Pessy as a name, and so won't have very many problems with teasing about it when they get older.
However, I'm not sure it's really a good idea in an English speaking context in neighborhoods where most people aren't familiar with it, especially for a non-Jewish girl whose parents don't have a very specific positive reason to tell her why they gave it to her. It's the sort of name that one needs to have a specific story of why you chose it to tell the child, to help her overcome any teasing she might get and make her proud of the name. This might not be necessary in a Hasidic neighborhood, but would be in most other places.