Interficio dixit:
How did this come to be named after Latin? My parents asked me this and I had no answer.
The fact that Central America was called Latin America makes it difficult for me to find latin books in libraries and catalogs as I often encounter hispanic cookbooks, and dancing lessons when looking for Latin stuff.
I would say the fact behind your difficulty is not the name Latin America, which by the way, encompasses all of South America and part of North America too, but the faulty library catalog. Because, in "latin books", latin = of or relating to the latin language. Whereas, in "Latin America", latin = of or relating to the latin people. Where are those libraries located, I dare ask?
Latin America, I concede, is not the most appropriate name for that mass of land, and one of the users in this forum was clever when he pointed out that Iberoamerica is a more suitable term. But consider the name given by your forefathers to the country where you live. They have expropriated the name of a whole continent, which extends itself almost from one pole to the other. And now Europeans use that word to refer not to a continent but to a single country. Brazilians understood it better, when they called their nation United States of Brazil.
The discovery, exploration, conquest and colonization of these lands was made by people coming from romance language speaking countries, long before a single germanic people touched its costs. In particular, Spaniards, in their thrust, almost embraced the whole of the two Americas, the enormous quantity of cities having Spanish names in the U.S. giving testimony to it (only consider how many cities bearing names beginning with "St", "San" and "Santa" you have on the west cost; not a surprise if one thinks the very name of the state that contains most of them, California, is of Spanish extraction).
Those romance languages descend from Latin, and the people who speak them are very often called Latins. What do you do if you want to refer to Spaniards, Frechmen, Italians collectively? You can do as I did above. But it's much more comfortable to use "Latins". So, historical reasons left aside, the name Latin America does not seem that inappropriate after all, Spaniards and Portuguese being Latins.