My aunt's cousin lives in America (with a green card). I want to travel to America, but I don't want to find a travel company. Can I get a visa in the name of visiting relatives?

No, because you are not immediate family members, only immediate family members can apply for visas in the name of visiting relatives. If you want to travel to the United States, don't say where your relatives or people you know are, or the immigration officer will think that you have an immigration tendency and will refuse the visa! I suggest you find a travel company to see if you can sign your name, and then go to play by yourself ~!