If I let a friend keep my vehicle that is in my name to drive can I insure them if they do not live with me in my household?

You should be able to list them as an additional named insured.  I would not think this would be a problem.  Contact your local insurance agent and inquire.  Best of luck. NOTE:  This response is general in nature and should not be considered legal advice.  No attorney-client relationship exists or is formed by this information.