Or they could just use a compound name after the whole intersection (especially if it's an interchange station like B/Y & Sh/Y), in which case the chances of having duplicate names go down dramatically (unless there are 2 or more intersections within the city in question where BOTH streets happen to have the same name).
In a hypothetical subway grid with a subway line running parallel to every east/west street as well as every north/south street, and an interchange station at every intersection of every east/west & north/south street, you can bet dollars to donuts every station would most logically be named after its respective intersection. It's the exact same concept as having every point on a 2D coordinate grid uniquely identifiable with a unique (x, y) coordinate.