Coming from a person who has BPD, I've been desperate in the past for my therapist to diagnose me and just put a name to what I've been feeling. To tell me that I'm not crazy, that I really do have anxiety or BPD. I think just having a label on it personally makes me feel better and gives me an excuse for my actions.
I believe that you're not making it up, but I also think that giving your symptoms a name isn't going to change a thing. Remember that you're going to therapy because YOU want to overcome these psychological hurdles. It's your life being affected whether or not you have it or not, so just try to get your therapists to not diagnose it, but to help you stay grounded. Because either way there is no cure for DID, like BPD, but there are ways to live with it. Techniques to stay grounded would benefit you a lot because I know in BPD people tend to 'float away' into thoughts while another part of them takes over. Try writing down your thoughts, especially when they start to stray. It helps A LOT.
I wish you the best. I know these diseases are so hard to overcome and require huge amounts of mental effort, but trust me you will get there. Never lose hope in yourself and no matter how much problems or diagnoses you get, never forget who you really are, who you really love, and what matters to you.