The movie never mentions where the story is set
The wikipedia article for Ghost Dog explains that the film never mentions exactly where the story is set, but it was filmed in Jersey City, New Jersey and the license plates in the film use fictional state nicknames for the state of New Jersey, USA.
The film was shot mostly in Jersey City, New Jersey, but the movie never mentions where the story is set. License plates reveal it is in "The Industrial State" and a vehicle from another state has on its license plate "The Highway State", both of which are fictional state nicknames.
Why are fictional names used?
Ultimately it seems the intent was so that viewers could believe that the story could take place anywhere. It could be in their own neighborhood or it could be in a fictional world. The location of the story is meant to be abstract and allegorical.
One article argues that using fictional names and never specifying the exact location of the story is done deliberately, to build the character of ghost dog into a believable urban legend.
It's never specified where Ghost Dog takes place. It was filmed in Jersey City, New Jersey (you can see the industrial sprawl of the Meadowlands from his roof). When Ghost Dog switches license plates on a stolen car, the plates read "THE INDUSTRIAL STATE" and "THE HIGHWAY STATE." There are some superficial indicators that Ghost Dog occurs in the New York metro (the Holland tunnel appears briefly), but the film could take place in any labyrinthine US metropolis. Ghost Dog could be moseying through your neighborhood.
While another article claims that the story is meant to be allegorical, hence the use of fictional names.
NYTimes Film Review
Ghost Dog's world is an abstract, allegorical place, where cars have license plates from "The Industrial State" and "The Highway State." From "Hagakure," the film quotes the standard Buddhist teaching "form is emptiness; emptiness is form," and Mr. Jarmusch sometimes seems intent on demonstrating the truth of this observation.