Original: The name has two different theories on how it was made, one being a mix of two suggestions, "The Rejects" and "The All Americans". The other being that it came from a song "Reject" by Green Day, with the chorus, "a reject, all american".
Simplified: The name All-American Reject was made from either a mix of two suggestions, "The Rejects" and "The All Americans" or the other being that it came from a song "Reject" by Green Day and had the chorus, "a reject, all american".