Yes, usually both spouses names would appear on the policy and insurance cards if both the husband and wife were insured under the same car insurance policy. Some companies simply put one individual as the named insured, but then list all drivers, spouses, and/or children. A policy contract does not have to list both husband and wife in order to pertain to both.
Normally if you are married you would want both spouses' names to be on the car insurance policy. It may be up to the procedures of the insurance company however if both you and your spouse will be driving the vehicles then both will need to be listed. If either you or your spouse is listed as the policyholder on the policy than the other would still need to be listed as a driver for the cars.
The guidelines and insurance cards and policy details of insurance companies due vary depending upon state laws and then the internal guidelines of an insurance company but typically if you and your spouse are insured on the policy both names would be listed on the policy and the insurance cards.
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If your current insurer only has you or your spouse but not both listed you should ask your agent why this is and if at your request it can have both names or not. As long as both are listed on the policy as drivers you are fine. Some companies just list one name as a named insured. For what your state laws on are this topic you can contact your state's insurance regulatory body for information. Usually an insurance department for a state will have a consumer division that you can get information from on your auto insurance policy, terms, rights, etc.
If you are newly married and need to combine your two car policies into one or just want to shop around for better rates, than click here for affordable auto insurance quotes. | 
