Does an auto insurance policy have to be in the same name as the car loan?

Lien Holders Insurance Indemnity Clause

Yes, Your finance contract (Loan) almost always requires that the borrower provide a Full Coverage Auto Insurance Policy on the vehicle being financed to protect the lien holders interest in the property until the loan has been satisfied. It's a matter of your finance contract. Failure of the borrower to provide the coverage required under the terms of the finance agreement puts the borrower in "Default" on the finance note subjecting the vehicle to repossession and other remedies at the lenders disposal.  

Include All Drivers

For Full Coverage, The Insurance policy should be properly in the name of the vehicle owner with any additional drivers listed as additional insureds on the policy. When the vehicle is still under a finance note. The finance company will generally require that the buyer maintain full coverage auto insurance until the note is paid. As this is part of the finance agreement signed by the buyer, failure to do so can subject the vehicle to repossession by the finance company.
 

Operators Liability

For liability only, any driver may obtain a liability policy for operation of the vehicle whether they are the owner or not, Since the Driver as well as the owner of a vehicle owner can both be held equally liable for any loss regardless of who is driving, most insurers will require you address the insured status of the owner as well.  

Owners Liability

In most cases the registered owner does have to be a named insured. But some companies may issue policies to anyone for any car, owned or not.