The first person to officially give the name "America" to the lands commonly known as the "New World" was a German geographer by the name of Martin Waldseemüller. This was inspired by Amerigo Vespucci, a Florentine merchant who accompanied an expedition to the New World several years after Columbus' voyage.
When Vespucci returned to Europe, he wrote glowing letters about the New World, which he believed to be a separate continent from that which had been discovered by Columbus. These letters were later read and published by German geographer, Martin Waldseemüller, who was the first to officially use Vespucci's name for the American continents. Amerigo was later Latinized to become America.