Vespucci gave his name to the Americas
He didn't name it after himself, but he was the first to refer to the Western Hemisphere as the New World. In 1507, Matthias Ringmann and Martin Waldseemuller used Amerigo Vespucci's name as the name of the New World for the first time.
They did so on the idea that Vespucci's published letters describing his trips to the New World had verified the existence of the Antipodes, which had been theorized since Greco-Roman times. As such, Ringmann and Waldseemuller believed it only fair that Vespucci's name be associated with the New World. The trend persisted, becoming permanent in the 1530s, when prominent mapmaker Gerardus Mercator labeled the New World as North and South America on his maps.