Every author has different reasons and ways to go about their pseudonyms. Kind of a let down, I know. But there is really no right answer. From pen names that are just initials (Hello, JK Rowling) to gender changes (Robert Gailbraith, also Joanne Rowling) or even complete persona changes (George Orwell is the author of Animal Farm, but is actually named Eric Blair). There are so many very famous ways to come up with an alter ego.