I apologize in advance, but I cannot really answer on behalf of peasants. However, I can answer on the general knowledge of the New World in Europe.

In 1507, a German Cartographer, Martin Waldseemüller, published a map with the discovered parts of the New World in Cosmographiae Introductio, which was the first to name America as well as show it as a New World. Martin and his partner, Matthias Ringmann, decided to name the continent America after Amerigo Vespucci, a Florentine explorer in the employ of the Portuguese crown from 1497 to 1502. This new map became widespread across Europe, resulting in Amerigo Vespucci becoming more famous than Columbus, at least among the aristocracy of Europe.

However, this was not the only reason. Compared to Columbus, Vespucci was much more prolific and elegant in writing accounts of his voyages to the New World. Whereas Columbus documented his journeys and treated his writings as documentary accounts, Vespucci described vividly the land and what it had to offer. Compared to Columbus's journals, Vespucci's were more widely circulated, in part due to Waldseemüller's map.

Source: Christopher Columbus, The Four Voyages

Mundus Novus (accounts of Vespucci's voyages)

Letters of Amerigo Vespucci The Medici Letter. Letter on his Third Voyage from Amerigo Vespucci to Lorenzo Pietro Francesco di Medici.