How far past the named insured the policy reaches is a property of the form, not of insurance generally, and one federal regulation shows three different answers. The Standard Flood Insurance Policy at 44 CFR Part 61 Appendix A contains three forms, each with its own definition of who "you" means. The Dwelling Form says "you" and "your" refer to the named insured or insureds shown on the Declarations Page "and the spouse of the named insured, if a resident of the same household", and adds that insureds also include any mortgagee and loss payee named in the Application and Declarations Page, plus any other mortgagee or loss payee determined to exist at the time of loss, in order of precedence. The General Property Form, covering non-residential and other risks, defines "you" as the named insureds shown on the Declarations Page with no spousal extension at all. The Residential Condominium Building Association Policy adds that the named insured "must also include the building owner if building coverage is purchased."
Three forms in one regulation, three different answers to "is my spouse covered". That is the reason a general rule about who counts is worth less than reading the definitions section of the actual policy.
Some people are insured because a statute says so, not because anyone listed them. Florida's no-fault law requires a complying policy to provide personal injury protection "to the named insured, relatives residing in the same household unless excluded under s. 627.747, persons operating the insured motor vehicle, passengers in the motor vehicle, and other persons struck by the motor vehicle" while not occupying a self-propelled vehicle. A person struck by the car has no relationship with the policyholder and is nonetheless within the coverage. Requirements of that kind are state-specific and coverage-specific, which is why the question "am I covered" is usually answered on the page for the particular coverage rather than here.
Where more than one name is on the policy, the order matters. The first name listed is the first named insured, and policies and statutes give that person or entity the role of the insurer's counterparty: receiving notices, holding the right to cancel, receiving return premium, and being the party the insurer is required to reach. New York's Insurance Law section 3426 illustrates the mechanics on commercial policies. During the first sixty days a covered policy is in effect, no cancellation becomes effective "until twenty days after written notice is mailed or delivered to the first-named insured at the mailing address shown in the policy and to such insured's authorized agent or broker"; after sixty days the notice period is fifteen days on the same footing. The state's Department of Financial Services has confirmed that notice to both the first-named insured and the broker is a condition of an effective cancellation, not a courtesy. California's Insurance Code section 662 shows the personal auto version, requiring notice of cancellation to be mailed or delivered "to the named insured, lienholder, or additional interest" at least twenty days before the effective date, or ten days where the cancellation is for non-payment of premium.
The practical consequence is that being second on a policy is not equivalent to being first. If the notice of cancellation goes to the first named insured's address, and that person has moved out, the other named insureds can find the policy gone without ever having seen a letter. On a jointly owned property or a policy that survives a separation, checking whose name is first and whose address is on file is worth doing before it matters.
Getting the name itself right is a substantive act, not clerical. The named insured has to be the party with the insurable interest in the thing insured. A house held in a trust and a policy naming only the individual, a rental property owned by a limited liability company and a policy in the owner's personal name, a vehicle titled to a business and insured personally: each of these is a mismatch between who owns the risk and who contracted for the coverage, and each is discovered at the claim rather than at the sale. A change of ownership, a marriage, a divorce, a transfer into a trust or the formation of an entity are the moments to check the declarations page rather than assume it followed along.