What it sounds like is happening is that your insurance company wants your general contractor's insurance company to have you named as an additional insured on their policy. That means that if they do something wrong during the renovation project their liability coverage also extends to you, the homeowner. Your insurance company doesn't want to have liability exposure if the general contractor messes something up and the injured party decided to sue everyone, including you the homeowner.
The general contractor needs to get in contact with their insurance agent and/or company and ask them about adding an additional insured to their policy. Some insurance companies charge to add an additional insured but most do not. Once the insurance agent or company processes this they will send a commercial certificate of insurance to their client, your general contractor, as well as directly to you usually as long as they are provided with your contact information, usually your email address. You can then forward this to your insurance company which ought to resolve the matter.
Putting the mortgage lender's name on the certificate of insurance really makes no sense. It is your name that goes on this commercial certificate of insurance because the contract is between you and the general contractor, not between your mortgage company and the general contractor. Your insurance company is also correct in that this is a relatively common request for homes that are being insured while vacant and being renovated. Your insurance company just wants their legal t's crossed and i's dotted so that they are not taking on liability exposure for something beyond their control.