Does the homeowners insurance have to be in the name of the person on the mortgage if they died?

If the Homeowner has died you should notify the Insurance Company. Any policy issues can be handled by the estate executor.

If you are an heir to a property in a jurisdiction that does not require transfer of deed until disposal you may purchase coverage as the owner.

You should also contact The Mortgage Company. The deceased may have purchased credit life option on the mortgage finance note at the time of purchase. If So, the credit Life insurance may pay off any remaining balance on an existing mortgage note.