Please name the quasi-Marxist philosophy advocated by Napoleon and Snowball.
I assume that you are asking what the philosophy is called in the book, not what it would be called in real life. If so, the name of the philosophy is "Animalism."
In the book, Old Major gives his speech in Chapter 1 that sort of plants the idea of rebelling and of overthrowing the humans. But then Snowball and Napoleon take his ideas and make them into something of a working philosophy. In Chapter 2, they flesh out his ideas to make the philosophy of Animalism.
This is meant to symbolize how Stalin and Trotsky and others made Marxism into communism.