Prior to any hearing and prior to beginning any investigation of the water problems of any specific portion of the State pursuant to Section 12616 or any investigation pursuant to Section 12617, the department shall give such notice to the agencies or persons likely to be interested as it deems necessary to afford every opportunity for the agencies or persons to be heard, and in addition to such notice shall give further notice of any hearing or investigation by mail to any city, county, state agency, or public district, deemed likely by the department to be interested, which has filed its official name and address with the department together with a request for notice.