Can a car be insured twice without the registered keeper knowing?

Are you serious with this question? No, the registered "Keeper" owner will get the bills in the mail or online. First, why would you want to insure a car twice and pay twice the bills for the same vehicle? Second, unless you own the car I doubt if you can insure it. You can pay the insurance bill if you wish but unless the car is registered in your name the bills and responsibility will go to the registered owner. Now it is NOT a good idea to provide insurance on anybodys vehicles except your own or/and your spouses.