Legal Question in Wills and Trusts in California

You can't change the name of the trust after one of the settlor's dies. Normally, its okay to leave the name of the trust alone, and just remove the deceased trustee, so that your mother is now the only trustee. If she doesn't like the name of the trust, she, as surviving trustor, could close the old trust and transfer the property to a new trust with the new name. But you have to read carefully the trust document to see whether the surviving spouse has the power to amend or revoke the trust after the first spouse dies.