Question: Who is the beach island that ends on the westernmost point with Jones Inlet named after?

Context paragraphs:
Barnegat Inlet: Barnegat Inlet is a small inlet connecting the Barnegat Bay with the Atlantic Ocean in Ocean County, New Jersey.  It separates Island Beach State Park and the Barnegat Peninsula from Long Beach Island.  The Barnegat Lighthouse sits at the northern end of Long Beach Island along the inlet.

Jones Inlet: Jones Inlet is located at the westernmost end of the 17 mi long Jones Beach barrier island that runs along Long Island's south shore.  The inlet separates Jones Beach State Park's West End from the community of Point Lookout and connects South Oyster Bay with the Atlantic Ocean.  In 2006, the inlet handled approximately 10,000 tons of commercial tonnage.

Bjargtangar: Bjargtangar is the westernmost point of Iceland and is considered the westernmost point of Europe outside the mid-Atlantic archipelago of Azores (which are often classified as remote islands).  It is the westernmost point in the timezone

Babylon, New York: Babylon is one of ten towns in Suffolk County, New York, United States.  Located on Long Island, the town population was 214,191 as of the 2014 census.  Parts of Jones Beach Island, Captree Island and Fire Island are in the southernmost part of the town.  It borders Nassau County to the West, and the Atlantic Ocean to the South.  At its westernmost point, its location is approximately 20 mi from New York City at the Queens border, and approximately 30 mi from Manhattan.  There is also a village of Babylon located within the town.

Short Beach (New York): Short Beach is the beach on the northern shore of the western end of Jones Beach Island.  The beach faces Great South Bay instead of the Atlantic Ocean, thereby providing some shelter from storm waves.  Since 1851 it has been the home of a coastal lifesaving station operated (at first) by the United States Life-Saving Service and later by the United States Coast Guard.  The current facility, Station Short Beach, typically does around 500 search and rescue missions each year —one of the busiest units in the Coast Guard's 1st District.  The Jones Beach State Park's West End Boat Basin is also on Short Beach.  The Jones Beach West End barracks of the New York State Park Police is around 200 feet south of the Short Beach shoreline.  An uninhabited islet, Short Beach Island, is usually just offshore, but occasionally connects to the beach when low tide exposes sandbars to the surface.

Jones Beach Island: Jones Beach Island is one of the outer barrier islands off the southern coast of Long Island in the U.S. state of New York.  It is named for Major Thomas Jones, who first came to Long Island in 1692, where he proceeded to build the island's first brick house near Massapequa.  Jones built a whaling station on Jones Island near the present site of Jones Beach State Park in 1700.  Jones Beach Island is sometimes referred to as Oak Beach Island and is the former home of the infamous Oak Beach Inn.

Faial Island: Faial Island (] ), also known in English as Fayal, is a Portuguese island of the Central Group (Portuguese: "Grupo Central") of the Azores.  The Capelinhos Volcano, the westernmost point of the island, might as well be the westernmost point of Europe, if the Monchique Islet, near Flores Island, is considered part of North America, for it sits on the North American Plate.

Reynolds Channel: Reynolds Channel, named after William Reynolds, is a strait in Nassau County, New York which separates the Long Beach Barrier Island, that contains the City of Long Beach, and the villages of Atlantic Beach and Lido Beach, from Long Island and Barnum Island.  The channel begins at the East Rockaway Inlet and ends at Point Lookout, where it merges with the Jones Inlet.  Four bridges cross the channel: the Atlantic Beach Bridge, the Long Island Rail Road's Long Beach Branch bridge, the Long Beach Boulevard Bridge, and the Loop Parkway Bridge.

Cape Wrangell: Cape Wrangell is considered to be the westernmost point of Alaska and all of the United States by direction of travel.  It is located on Attu Island, which is situated in the Near Islands.  Following this definition of westernmost, an alternative westernmost point would be located on the tiny (ca. 200m diameter) Peaked Island, just off the coast to the west, but because both sit west of the 180th meridian, these two are at times viewed as the easternmost points of the United States.

Loop Parkway: The Loop Parkway (also known as the Loop) is a 2.65 mi parkway in Nassau County, New York, in the United States.  It serves the barrier islands south of Long Island itself, beginning on Long Beach Barrier Island at an intersection with Lido Boulevard in Point Lookout.  From here, it heads generally east–west across Alder and Meadow islands to an interchange with the Meadowbrook State Parkway on Jones Island, a part of Jones Beach State Park located just north of Jones Beach Island.  The islands served by the Loop Parkway are separated by narrow channels of water, all of which connect to Jones Inlet.  The parkway is maintained by the New York State Department of Transportation (NYSDOT) and inventoried by the department as New York State Route 908C (NY 908C), an unsigned reference route.

Supporting paragraphs: Jones Inlet Jones Beach Island
Answer: Major Thomas Jones