yes, back then they are not divide into North America, Central America, or South America. Back then they are just a one big continent called "The New World" by the Spanish, then the French, and later the English also adopted this term. They all called the new continent as "The New World". The land later on (after all the exploration was done) divided to regions and renamed to North, Central, and South Americas that we now have.
Yes, there is a lot of people in that second part of Grand Line or "The New World" as they called it. However, the land and island are not yet 100% has been explored especial no one except Roger found Raftel yet. But i don't think that 100% why they called this second part of GL as "The New World". I think there is one more factor that contribute to this name that is the gathering of people (both private, traver, goverment officer), who has the power to change the world to bring the world to the New Age, that we sometime heard in One Piece (Dragon, Lofulamingo, Black Beard, Shanks, Coby say about the New Age).
One more interesting about One piece that i notice, "If you use the One piece world, or at least the area that SH crew travel, and fix it to our world map, you will find a lot of place that match with each other. If you do this i believe you will find the final location of Raftel in our world map. any guess on where is that "Raftel" in our world map will be? The answer is nothing new, but it may surprise you. Let's take a guess and i will tell you later on after all of your guess finish. I want to see how many of you will say the same think with what i have in mind. But please remember, it is just my guess, i could be incorrect, too.