Would being obsessed with something that you don't believe in be considered OCD, or is there another name for?

There's a difference between obsession and compulsive obsession. If you are obsessed with ANYTHING, then well, you're obsessed. OCD is basically the compulsion to do something over and over. One might say, "Bill is OCD about people taking off their shoes when they enter his house. He sometimes even lays down paper towels wherever people walk so as to not dirty the carpet."