Last Name Issue

My last name was put in wrong through a third party booking site. I checked my email today to go over everything since we fly out tomorrow. Of course it was listed incorrectly.

Customer service rep said my options were to 1) make a new reservation away from my husband
2) check in with the ticker counter before my flight tomorrow

Would they be able to change it that close to the flight? I just don’t want to be screwed over that close to our flight

Thanks!