This could be translated as “Office of the Chief Judge—Civil Docket and Case Assignments Section.” In the organization of courts in Spain in areas where there are many “juzgados” together in one district, there is a “juez decano” who is elected by his fellow-judges on the “Junta de Jueces” to oversee the administration of the courts. This is the Spanish counterpart of the chief judge (not to be confused with “chief justice”) of U.S. federal district courts. So “decanato” is the “Office of the Chief Judge.” One of the sections supervised by the “decanato” is the “Oficina de Registro y Reparto Civil” where civil cases are docketed (“registro”) and assigned (“reparto”) to a specific court for trial and adjudication. In other respects, the “Comisión Oficial de Notificaciones y Embargos” is a section that centralizes all of the courts’ “notificaciones” (service of process and court orders in general) and “embargos” (court-ordered attachment of property).
A description of this process can be found in "Guía orientativa sobre la Justicia en la Comunidad de Madrid." Madrid: Vicepresidencia Segunda y Consejería de Justicia e Interior, 2003. For a description of the duties of a U.S. federal chief judge and the organization of the Office of Chief District Judge, see "Deskbook for Chief Judges of U.S. District Courts," Washington: Federal Judicial Center, 1993.