I have a better idea. Let’s call it The Federal Reserve.
One of the facade parties we can make appeal to one half of society and the other we can make appeal to the other half of the society to make commoners think they are both choosing, having a say, and can feel virtuous about their fake choice opposed to the folks who chose the other faker party.
There can even be meaningless elections where the people can choose between the things the uniparty was going to do anyways like killing people.
Eventually we can just call it The Party and we can be at war with Eurasia, as we always have been.
I thought we are there already. :)