Okay kiddo, so a long long time ago, before there were any people living in the Americas, the landmasses we now call North and South America had different names. North America was actually called Turtle Island by some Native American tribes because they believed that the continent sat on the back of a giant turtle that swam in the ocean. South America was called something else, we’ll get to that later.
Then many years later, certain people from Europe (like Christopher Columbus) sailed across the big water (the Atlantic Ocean) and landed on the shores of the Americas. Columbus thought he had reached the shores of the East Indies, which was a group of islands in Asia that Europeans traded with for things like spices and silk. So he called the people he met “Indians.” But that was not the right name for them.
Eventually, more and more Europeans came to the Americas and started to explore and trade with the indigenous people who had been living on these lands for thousands of years. These Europeans also started to claim these lands as their own and give them new names. They named the continents after Amerigo Vespucci, an Italian explorer who realized that Columbus had not reached the East Indies but had actually discovered a “New World.” So, the continents were named the “Americas” in his honor.
The term “South America” was used to describe the southern half of the continent, while the “Latin America” came much later and was used to describe the countries in South America that spoke languages (like Spanish, French, and Portuguese) that were derived from Latin, the language of the Romans.
So that's how the Americas got their names, from a combination of mistaken identity, exploration, and claiming of land. It’s important to remember though, that these names were given by outsiders, and the original inhabitants of the Americas had their own names and identities before the arrival of Europeans.