Final answer:
The Italian explorer Amerigo Vespucci is the namesake for both North and South America, and this was first reflected in Martin Waldseemüller's 1507 map that labeled the continents 'America'.
Step-by-step explanation:
The namesake of both North and South America is the Italian explorer Amerigo Vespucci. Unlike Christopher Columbus, Vespucci recognized that the lands he explored were part of a new continent, separate from Asia. This realization was captured in the writings of his voyages, which were widely read among Europeans. As a result of his insights and the published accounts of his travels, the German cartographer Martin Waldseemüller labeled the new continent 'America' on his map in 1507. This name was in honor of Vespucci and has been used since to refer to the combined landmasses of North and South America.