Any person can change their name, and any parent may change the name of their minor child. It is done by Petitioning the Court for a name change, and submitting an affidavit to the effect that such name change is not being sought for the purpose of alluding creditors or otherwise avoiding a legal duty.
All parties who may have an interest in this name change need to be noticed of the Petition for a Name Change, and quite often, a Notice of Intent to Change name is published in the local newspaper.
Of course, during a divorce proceeding, a party may be restored to their Former/maiden name as part of the Final Decree of Divorce.