The clerk shall record a certificate of partial satisfaction or a certificate of satisfaction on the grantor index, both under the name of each grantor on the underlying deed of trust and under the name of the first-named trustee under which the deed of trust was indexed, all as identified on the certificate of satisfaction. The deed book and page number or the instrument number of the released deed of trust shall also be designated in the index. Any clerk using a separate index book or data file for grantees only shall also record in such book or file the name of each grantor on the underlying deed of trust as identified on the certificate of satisfaction.