There were not that many people who have their names actually associated with American imperialism. It was more of a nationwide trend than something that was pushed by just a few people. I will mention two people who were quite important in US imperialism.
First, there was Alfred Thayer Mahan. Mahan was a naval officer who wrote an important book entitled The Influence of Sea Power Upon History. This book put forth the idea that naval power was the key to a country's success. This idea influenced many people to argue that it was important for the US to take an empire that would allow it to project naval power over long distances.
Second, there was Theodore Roosevelt. Roosevelt was a staunch supporter of the idea that the US needed to take an empire. He felt it was important to do this so as to give Americans a chance to flex their muscles and act in a masculine way. He felt that America had to challenge itself so that it would continue to be strong.
These are two of the most important names in American imperialism.