Why does Napoleon use Snowball's name to control the animals?

It’s clear in the early chapters of Animal Farm that Napoleon and Snowball had different ideas of what to do with the farm after their revolution. Both pigs weren’t going to be able to lead together, and Napoleon successfully exiled Snowball through the use of his trained dogs. To put this in Russian terms, as Animal Farm is an allegory of the rise of Communism in Russia, Stalin (Napoleon) takes over in the USSR after the death of Lenin (Old Major), and Trotsky (Snowball) is exiled for a series of political disagreements. He is later assassinated in Mexico. Stalin is well-known for taking out his political opponents through an extensive network of supporters, spies, and secret police, which the dogs represent.
In the context of the book, bringing up the image of Snowball does two things for Napoleon’s image. First, it makes Snowball a scapegoat. Every mistake and every problem, up to the destruction of the windmill, is blamed on Snowball. It’s ridiculous to think a tiny pig, acting on his own, could take down such a large construction project, but the animals buy it. Secondly, it helps Napoleon control the other animals through fear. Snowball becomes a kind of boogeyman for the other animals on the farm, and they are coerced to things, because if they don’t, the punishment is Snowball’s return. “Do you want Snowball to come back?” Squealer asks them, several times over, until they do as they’re told.
While Snowball is gone for good, the character still plays a very important role. Unfortunately for him (and Trotsky), he was more useful to Napoleon in his absence than he ever was in his presence.

After Napoleon usurps power and banishes Snowball from the farm, he develops into a tyrannical ruler who makes the animals work long hours while simultaneously reducing their food rations. As leader of Animal Farm, Napoleon employs a pig named Squealer to act as his mouthpiece and spread propaganda in his favor. Whenever anything goes wrong on the farm or Napoleon makes a costly mistake, he and Squealer place the blame on Snowball. Napoleon essentially uses Snowball as a scapegoat to shift the blame and hide his mistakes. Napoleon ends up blaming Snowball for colluding with neighboring farmers to attack Animal Farm and destroying the windmill. By using Snowball as a scapegoat, Napoleon successfully manipulates the animals into believing that he is always in the right while bolstering the hysterical atmosphere on the farm. Napoleon earns the animals' confidence by presenting himself as a faultless leader and courageous protector, which significantly increases his control over the animals.