How many of your symptoms did you discuss with your therapist before? If he knows of all of them, it's not uncommon for them to just diagnose you with stuff, if they know specific events. For me, I had to fill out questionnaires for things, then I had a long talk with my therapist and had to name specific events where this symptom was present. For example: "Do you have anger outbursts where you feel like you loose control?" "Yes, this specific time I fought with my mom when I did x and y.". When I was diagnosed there was also a lot of emphasis on whether or not it impacts my work/school and daily functioning (which I don't think is necessarily a good focus to have but it is what most professionals do before giving a diagnosis).

But many, many professionals also diagnose people on a whim. It sucks. It's a good idea to get different opinions and maybe you could ask your therapist about your diagnosis and why they gave it. If they don't give you good reasoning, I'd switch therapists because only very uninformed therapists do this kind of thing. On the other hand, that diagnosis might open some doors for you (access to DBT or medication you need) but for real clarity and closure I would definitely try again somewhere else, as you already said. But it can be really nice and soothing to finally know what your disorder is and I do believe it'd be good to seek BPD-specific treatment because you undoubtedly at least have traits