No, you cannot restore the legal use of your maiden name through a Separation Agreement, which is merely a contract between two persons.
To change your name in a legal sense, you must petition the court.
To return to the legal use of your maiden name, you must either:
– file for Divorce and petition the court to restore your name through that proceeding; or
– you may petition the court using the types of “name change” legal documents detailed at a site like American Legal Review.