The Common Policy Conditions the exam names are cancellation; changes; examination of your books and records; inspections and surveys; premiums; and transfer of your rights and duties. One idea runs through several of them: the first named insured, the insured listed first in the declarations, acts for everyone on the policy.
Cancellation: the first named insured may cancel the policy by notice to the insurer, and the insurer may cancel by written notice. California limits the insurer. Under Insurance Code §676.2(b), once a commercial policy has been in effect more than 60 days, or right away if it is a renewal, the insurer may cancel only for the grounds the section lists. Nonpayment of premium is one, and it includes a payment due on a prior policy from the same insurer, due during the current term and covering the same risks.
Notice: §677.2(c) requires at least 10 days' notice when the insurer cancels for nonpayment of premium. Most other grounds need a 30-day notice.
Changes: the policy contains all the agreements between the parties. The first named insured may request changes with the insurer's consent, and the terms change only by an endorsement the insurer issues. California again limits what the insurer may do on its own midterm: after 60 days, §676.2(c) allows a midterm change such as reducing a limit only for a permitted reason, such as a material change in the risk, with written notice at least 30 days ahead to the named insured and the producer of record, stating the effective date and the reasons.