In California, how do we only have one spouse sign for the mortgage?
The lender is looking for a way to protect its interest in the house should you default on the loan. In a community property state such as California, the spouse who is not a party to the loan could claim a 50% interest in the house, especially if marital money/salaries was used to pay the mortgage. We are not familiar with the term "financial separation" outstide the context of a court proceeding for a divorce or legal separation.
In California, a husband and wife can hold property together as joint tenants or tenants in common, or the property may be community property. No two of these forms of ownership can exist at the same time. A husband and wife also can own property separately. In general, all real property acquired during a marriage and situated in California is community property. A leasehold interest is not considered community property, nor is property owned by either spouse before marriage, or property acquired by either spouse during marriage by gift or inheritance. Subject to certain exceptions and restrictions, either spouse has the power to manage and control their community property, and each spouse can devise their one half share in the community property by will. Income and profits on separately owned property remain with the separate property.
If you do not intend that your spouse be on the title, a community property disclosure should be executed. The lender may have a form available that would satisfy their particular needs.
It may also be possible for the non-owner spouse to transfer his/her interest in the property via deed to the other spouse. Proper drafting of any such documents will be critical therefore it would be recommend that you seek the advice of a local real estate attorney.