C.S. Lewis’s lifelong childhood nickname was Jack.
Lewis was born Clive Staples Lewis, but he disliked being called Clive. As a child, he chose the name Jack after the death of a dog named Jacksie, an animal he had loved deeply. The nickname gradually became shortened to Jack, and it was the name used by people close to him.
The name is especially visible in accounts of Lewis’s friendships with J.R.R. Tolkien, Charles Williams, and Owen Barfield. These writers belonged to the informal Oxford literary circle known as the Inklings. They discussed manuscripts, mythology, theology, and literary craft, often meeting at the Eagle and Child pub, which they nicknamed the Bird and Baby.
“Jack” was not a pen name for Lewis’s published works. He normally wrote as C.S. Lewis, a form based on his initials. Warnie, meanwhile, was the nickname of his older brother, Warren Hamilton Lewis, so it is a common but incorrect answer to this question.