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Here is the MS law that explains how you have to sue and name the vital statistics office to get the name change.
Currently there is no form provided by the vital statistics office and you must call them to start the process :
To make corrections or to make changes to a birth or death record, contact the Corrections Department at 601-576-7981.
SEC. 41-57-23. Proceedings to correct birth certificate containing major
(1) Any petition, bill of complaint or other proceeding filed in the
chancery court to: (a) change the date of birth by two (2) or more days, (b)
change the surname of a child, (c) change the surname of either or both parents,
(d) change the birthplace of the child because of an error or omission of such
information as originally recorded or (e) make any changes or additions to a
birth certificate resulting from a legitimation, filiation or any changes not
specifically authorized elsewhere by statute, shall be filed in the county of
residence of the petitioner or filed in any chancery court district of the state
if the petitioner be a nonresident petitioner. In all such proceedings, the
State Board of Health shall be made a respondent therein, and a certified copy
of the petition, bill of complaint or other proceeding shall be forwarded to the
State Board of Health. Process may be served upon the State Registrar of Vital
Records. The State Board of Health shall file an answer to all such proceedings
within the time as provided by general law. The provisions of this section shall
not apply to adoption proceedings. Upon receipt of a certified copy of a decree,
which authorizes and directs the State Board of Health to alter the certificate,
it shall comply with all of the provisions of such decree.
(2) If a child is born to a mother who was not married at the time of
conception or birth, or at any time between conception and birth, and the
natural father acknowledges paternity, the name of the father shall be added to
the birth certificate if a notarized affidavit by both parents acknowledging
paternity is received on the form prescribed or as provided in Section 93-9-9. The
surname of the child shall be that of the father except that an affidavit filed
at birth by both listed mother and father may alter this rule. In the event the
mother was married at the time of conception or birth, or at any time between
conception and birth, or if a father is already listed on the birth certificate,
action must be taken under Section 41-57-23 (1) to
add or change the name of the father.