I'm not sure about how accurate/up-to-date that map is.. I looked through a bunch of different zoning and development maps and charts on both, ZoLa and NYC Planning for that area going back as far as I could find docs and didn't see a single reference to these driveways by that name.
Before the construction of this apartment complex these used to be Wooster and Greene Streets. But documents dating back to at least 1956 explicitly crossed out those names.

Looking at that map around my home neighborhood I found at least one street name that also does not exist. When I saw it in OSM, I walked over there and asked people who live in homes on that "street" if they knew anything about that name and they had no idea what I was talking about. All the homes there had address of the main street nearby.

The point is, I'm not sure that "more data" coming from that map is "better data". I'd trust a more precise, narrower scope maps from NYC itself rather than a US-wide amalgamation map.