I was always taught we got the name from the Italian explorer and navigator Amerigo Vespucci. He was from the Republic of Florence and participated in at least two voyages of the Age of Discovery between 1497 and 1504, first on behalf of Spain and then for Portugal.
“ the Italian explorer and navigator Amerigo Vespucci”
After he returned from his exploratory voyages, two booklets, including drawings, were published under his name. I guess that publishing paid off in his lasting fame, at least his name.
I’m of the opinion that we were lied to about Amerigo Vespucci.