Can I be a policyholder for car insurance in this situation?

You state:  "If both names are insured.....? "

NAMES are not insured.  VEHICLES are insured.Besides, because you are married it makes no difference whose name happens to be listed as the policyholder......and.....anyone can pay the premium. 

Read the policy, I think you will find that both of you are listed as regular drivers of the insured vehicle.

And........I think someone gave you bad information about the policyholder name(s) 

If you don't own the car, you can be listed as a driver.  You could amend the title &/or registration to both of your names to be added as the joint policyholder, but that isn't free, it might not be worth the expense.  

They should add your name on the policy too.   Did they list you as a driver ?

What they said makes no sense.   Call and ask again.    If you can sign on to the insurance companies website and log into your account you can make changes that way. 

No.  You can't insure what you don't own.  In the eyes of the insurance company this is no different from you insuring my car.

Title = insured.

Call & ask them.

The only issue I see is they would prefer them to be the same because in the event the car is totaled, who do they pay?

" It s just easier for me to switch things out if I need to, pay the bills, etc.

Teach your wife to be capable,

You might not always be there to be the PRINCE (or controller depending on how you look at it). 

Call the insurance company.  It will be easier if your name is on the title too.