You should read carefully when signing the contract.
I suggest you go now, clarify the situation and change your name.
It is also allowed to pick up the car with a contract when picking up the car, so it doesn't matter if the name is wrong. You can only pick up the car after reading the contract.
The title certificate is not important. You signed your name when you picked up the car.
The driving license was made only after you got on the license plate.
So please rest assured that it won't have any impact, but try to change the name to avoid unnecessary trouble.