Named after the town of Blue Point, Long Island, situated on the Great South Bay. This was the center of the Long Island oyster business for many many years.

From the blog Frost Street: The Culinary Adventures of a New York Lawyer:

"Named for a town on the Great South Bay of Long Island, Blue Points were the prize of the American oyster harvest for nearly a century. Queen Victoria preferred them above all other varieties; for a time the fishermen of the south shore shipped over a hundred thousand barrels of the shucked treasures every year. The reputation of these magnificent shellfish spread so wide that counterfeiting and theft took hold; the state legislature had to impose one of its first and only origin control appelations on them, and rampant poaching led native fishermen to attempt secession. As with the Kumamoto, the Blue Point oyster has deserted its namesake locality. Encroachment of tidal waters in the first half of the twentieth century raised the salinity of the Great South Bay to the point that its oysters could neither grow healthily nor avoid salt-water predators. Today, the term "Blue Point Oyster" can be used for any east coast oyster of the species once found at Blue Point, but is often used to denote a Long Island oyster..." Read more here >