It should be no problem for your parent to gift you a car and sign the title over to you. I believe you would just fill it out as if you are buying it for $0.00

You may still have to pay some amount of fair value tax on it when you title it in NJ but I’m not 100% sure. If your dad has easy access to a notary it might be worthwhile to have him get a letter saying he is gifting it to you and that he is your father. You shouldn’t need it if your last names are the same but it’s better to have it ready just in case