You can use a search engine to look up your states name change law. In many states this will require public posting (newspaper) and notification of your parents (even if mom helps with this, dad will be notified, and he will have the opportunity to object to any change). You don't have any legal right, at the age of 13 to do anything on your own, or assert any type of independence in the legal arena. Standing up to dad isn't going to get you very far.

For the record, changing your name doesn't change who you are, nor your parentage.