(b) Upon the filing of the petition for name change, notice shall be given to the child's mother and to the child as provided by the Alabama Rules of Civil Procedure. Notice may be waived as provided by the Alabama Rules of Civil Procedure. The child's mother shall, within 30 days after receiving notice, file her objection or consent to the name change with the probate court. The probate court shall appoint a guardian ad litem to represent the child if the mother files a timely objection or if the court determines such appointment to be in the best interest of the child. Following receipt of the mother's response or upon expiration of the time for her response, the probate court shall conduct an informal hearing at which all interested parties may present evidence for determination of whether the name change is in the best interest of the child. The court shall issue an order of name change or denial of name change. Upon change of the name of the child, a certified copy of the minutes of the court shall be sent by the judge of probate to the Office of Vital Statistics, State Board of Health, and to the Registrar of Vital Statistics of the county where the petition was filed within 30 days after the minutes are recorded.