I think the idea was to have two-letter designations for Starfleet ship types (all starting with N for Navy) and single-letter designations for civilian/commercial designs.
The Stingray is designated "NY-01," which I think means it's a "'something' gun ship" if the wikipedia page on hull classifications is accurate.
Maybe "gun ship (nuclear-powered)?"
The real world answer is that Gene Roddenberry wanted the Enterprise to have a hull number similar to aircraft tail numbers, which is where the NCC-#### designation came from. The with the Excelsior they introduced NX-#### for experimental and/or class leaders. The NX "class" is a bizarre exception because one of the show runners wanted it that way.Can't find much that seems to fit NY, I think it would make more sense for Star fleet to come up with it's own, the N is Navy, marking it as a Military ship, and the Y is for Patrol/gunships. The X can be Exploration.
I don't know how it's being handled in the quest is going to handle it, but in Canon there are only NX and NCC designations and I don't think there's an acronym or in universe reason for NCC.