Mandatory Insurance Question

I have a lien on my car for a loan through American General Finance. The car has full coverage through GEICO. American General says that, unless I tell GEICO to make them the payee on any claims, they will take out a seperate insurance policy and charge me for it. Can they do that? Their interest is protected aleady through the GEICO insurance. If I submit a claim for a broken window or call a tow truck, I don't think that everything should have to go through American General.

Yes, the creditor can make that demand.