S.D. Codified Laws § 34-25-15
In cases of legitimation, the department, upon receipt of proof of the marriage of the parents after the birth of the child together with an affidavit of paternity signed by both parents of the child, shall prepare a new certificate of birth in the new name of the legitimated child.
Within ten days after the filing of an affidavit of acknowledgment of paternity, signed by both putative parents who are not married, the department shall add the name of the father to the certificate of birth if paternity is not shown on the record. Upon request of the parents, the surname of the child may be changed to that of the father or a combination of mother's and father's surnames, in which case the department shall prepare a new birth certificate. A change in paternity, which is already shown on a birth certificate, may be made only upon receipt of a court order determining paternity.
Upon receipt of a court order or affidavits determining the paternity of a child pursuant to § 34-25-13.1, the department shall prepare a new certificate of birth. Each applicant for a new birth record shall submit a five dollar fee to the department for the preparation and filing of the record.
SDCL 34-25-15