AirBnB put my name in wrong on a reservation [Vancouver]

I booked a hotel through AirBnB (never doing this again) and when I called the hotel after receiving the confirmation to confirm something about my reservation they had absolutely no record of my reservation even with my confirmation code and said I needed to call AirBnB. I did, they said it’s confirmed and I needed to call the hotel. After a day of back and forth with the hotel and AirBnB, AirBnB finally said the reservation wasn’t there because my middle name was put as my last name which is why the hotel couldn’t find the reservation. I suspect this was done during the ID verification process on their end, since I don’t put my middle name in reservations for hotels or rentals.

Now, I definitely do not trust the hotel or AirBnB will have my reservation when I arrive, and I don’t want to be stuck in a city I’m not from with nowhere to stay or have to fight with both customer services again to find it. I told AirBnB I want a refund and to cancel the reservation because of this is whole issue and they said no. You can cancel it but we won’t refund it because we’re seeing the reservation is confirmed.

I really don’t trust this, considering if I hadn’t called I would not have known this until I showed up. Do I keep calling Airbnb about this until they agree? Or do I just dispute this with my credit card since they already charged me for the stay? I can’t afford to be out this money, but I also can’t afford to be trying to find a hotel on a busy weekend late at night in a city I’m not from.