In 1507, 15 years after Columbus sailed the ocean blue, a group of scholars made the Waldseemuller map showing the land he was exploring as a separate landmass and not a part of Asia as Columbus believed.
How did they know this years before any European saw the Pacific Ocean? no idea. But they had been reading the writings of Amerigo Vespucci and dubbed the New World "America". I guess that because they were right about that whole, the New World is not connected to Asia thing, people figured they were right about what to call it too.
image from the Atlantic.
new book on the subject, Toward the Setting Sun: Columbus, Cabot, Vespucci, and the Race for America