Well more likely the names came from Vespucci.

ORIGIN the name America dates from the early 16th cent. and is believed to derive from the Latin form ( Americus) of the name of Amerigo Vespucci, who sailed along the west coast of South America in 1501.

I can hear it now - in best Italian laugh

Oh no I ran into this pice of shiit land , I'll call it America ! (then he sailed North) Oh no another pice of shiit land I'll call this one North America.

He then went back to Italy to brag about his new found pieces of shiit . Later he set sail again to the south but this time steering clear from the other America shiit.

Oh no whats this pice of shiit land (now out of America names) I'll call this one Australia laugh