"I just saw this today on a restaurant sign: Field of Green's -- is the name of the eatery. Now, they can call it anything they want, it's their place. But the name implies that it belongs to Field of Green, not that it is a field of greens. Oh well, whatever."
To me, that name is the same as saying Green's Field. That is, a field that belongs to someone named Green. I agree that it's probably not what they meant, though.