S.D. Codified Laws § 38-8-34
Petitions for changing the names of districts organized under this chapter may be filed with the State Conservation Commission. Any such petition shall be signed by a majority of the district supervisors and shall state the present name of the district and the proposed new name. If the commission determines that the proposed new name is not identical with or so similar to that of any other district in the state as to lead to confusion or uncertainty, it shall present a statement of such determination to the secretary of state, who shall issue to the district a certificate, under the seal of the state, evidencing the change of name of the district. Upon the issuance of such certificate, the supervisors of the district shall cause due notice to be given of the change of name of the district.
SDCL 38-8-34