From Wikipedia:
----
Vespucci's voyages became widely known in Europe after two accounts attributed to him were published between 1503 and 1505. The Soderini letter (1505) came to the attention of a group of humanist scholars studying geography in Saint-Dié, a small French town in the Duchy of Lorraine. Led by Walter Lud, the academy included Matthias Ringmann and Martin Waldseemüller. In 1506, they obtained a French translation of the Soderini letter as well as a Portuguese maritime map that detailed the coast of lands recently discovered in the western Atlantic. They surmised that this was the "new world" or the "antipodes" hypothesized by classical writers.[44] The Soderini letter gave Vespucci credit for discovery of this new continent and implied that the Portuguese map was based on his explorations.[45]
In April 1507, Ringmann and Waldseemüller published their Introduction to Cosmography with an accompanying world map. The Introduction was written in Latin and included a Latin translation of the Soderini letter. In a preface to the Letter, Ringmann wrote
I see no reason why anyone could properly disapprove of a name derived from that of Amerigo, the discoverer, a man of sagacious genius. A suitable form would be Amerige, meaning Land of Amerigo, or America, since Europe and Asia have received women's names.[46]
The Introduction and map were a great success and four editions were printed in the first year alone. The map was widely used in universities and was influential among cartographers who admired the craftsmanship that went into its creation. In the following years, other maps were printed that often incorporated the name America. In 1538, Gerardus Mercator used America to name both the North and South continents on his influential map. By this point the tradition of marking the name "America" on maps of the New World was secure.