And in any state, police do not always follow the law, and refusing to give your name may make them suspicious and lead to your arrest, so use your judgment. If you fear that your name may be incriminating, you can claim the right to remain silent, and if you are arrested, this may help you later.nd in any state, police do not always follow the law, and refusing to give your name may make them suspicious and lead to your arrest, so use your judgment. If you fear that your name may be incriminating, you can claim the right to remain silent, and if you are arrested, this may help you later.