Basically, in the U.S., you can use any name you want as long as you are not trying to "defraud". The situation you describe, under this description, makes it illegal as you are defrauding the events you are trying to get in to, since you are misrepresenting your association with AP.
If you want a press pass, as mentioned above, just make one up yourself as a "Freelance Photographer" working for your own photography business. This is not illegal and widely used and accepted, according to my photography course, NYIP. My wife has one that they issued her for the Professional Course. I can request one if I want, but I have one with the company that I am associated with here in Texas.
The main thing I see here is that you are doing something both illegal and unethical. Please reconsider your actions.
Just my understanding of the situation.
Ken