The lady i bought my golden from said she was a purebred. She gave me the paper to mail in to register her. She said they would send me my papers on the new puppy. I don't know how the process works, is this true?

Yes. You fill out the paperwork she gave you, include your check to register the dog mail it in and the AKC will send you back the paperwork or your registration papers. This way you have picked out a name for your dog and that registered name is your dog's name exclusively. It's like you have reserved that name until the AKC sends back the paperwork. You will notice that you must make at least 3 choices for the dog's name. Be sure to make it a long name of at least 3 or 4 different words like "Lady of the Manor Blue Jeans" so that you will essentially "get" that name.