Answer:
It is not true that Amerigo Vespucci liked the New World so much that he asked Martin Waldseemuller, a map maker, to name it America after himself. On the contrary, Martin Waldseemuller named the continent in honor to him, but not at his request.
Explanation:
Amerigo Vespucci was a Florentine banker, diplomat and explorer who, in Spanish and Portuguese service, explored parts of the continent of America.
Vespucci wrote some letters in which he spoke highly of the fertility and beauty of the continent he had traveled to. These letters were in great demand in Europe, and led the Europeans to discover that what had been discovered in the west was not isolated islands or part of the Indies but a 'New World' (this term is from Vespucci himself, one of his letters was entitled Mundus Novus). These letters were a reason for the German cartographer Martin Waldseemüller to name the discovered land after Vespucci on his map Universalis Cosmographiae in 1507.