First of all, you call it a mortgage, but most likely do not have a mortgage. Although California law allows for mortgages, the security instrument of choice in California is the deed of trust, not the mortgage. The difference is important. Mortgages, unless they contain a power of sale, require a lender to file an action to foreclose when the debtor defaults. A deed of trust, however, contains a power of sale, which can be exercised by directing the trustee to sell the property, without the necessity of an action to foreclose. When I say action, I mean an actual lawsuit. Trustee's sales are commonly called nonjudicial foreclosures.
Second, your terms are erroneous. The mortgagee is the party who holds a mortgage, and is the one lending the money. The mortgagor is the borrower, and the one who is occupying the house during the terms of the underlying obligation.
These terms are important. When a mortgage is assigned, the assignment must be recorded. (Civ. Code, sect. 2932.5.) That provision does not apply to deeds of trust, however, as long as the trustee is properly substituted.