Is it permissible to give false information to the police to avoid accountability when wearing the hijab in a country that prohibits it?

Lying is a reprehensible sin that a believer does not resort to, yet it may be permissible at times if it is the only way to achieve a praiseworthy objective, and it becomes obligatory if the attainment of that objective is obligatory.

Therefore, if providing your real name to the police would cause harm to you or your family, or prevent you from wearing the hijab, then there is no blame upon you for giving them false information.