Whether you have a seat cover or not, you should always tie your dog correctly, according to the law. This is why the vast majority of models are designed to leave space for seat belts. Your pet should wear a harness that is attached to your vehicle's seat belt fasteners. In any case, do not attach it by the collar.
You also have the option to put your dog in a spacious and comfortable carrier for greater safety. Use the seat belt to maintain that carrier in place. Another possibility is to have your dog wear a double-hook harness through which you can pass the safety belt. Finally, there are divider grids that offer safety and comply with regulations.