I'm not aware of any U.S. state that requires Many U.S. states do not require personal vehicle drivers to be insured. I.e., with the exception of some commercial classes of vehicles, the law only requires that cars driven on public roads be insured (to levels specified by law or regulation).
In every case I have encountered, state insurance regulators do allow insurers to assess premiums based on the owners and drivers of insured cars. Therefore, you must review the insurance policy to ensure that your use of the car complies with its terms. Policies will usually have exceptions or guidelines for when "occasional, casual, or intermittent" drivers must be declared.
If an undeclared driver has an accident, and the insurer determines the driver should have been declared, then the insurer might cancel its coverage or increase the premiums charged to the owner. Both the driver and the owner could even find themselves without insurance coverage for the incident.