The first name in C.S. Lewis’s nickname “Jack” was Clive.
Lewis was born Clive Staples Lewis, but he rarely used “Clive” in adult life. He and his brother Warren used “Jack” as Lewis’s everyday name, and many of Lewis’s closest friends continued to use it. The nickname is associated with an incident from his childhood involving a dog called Jacksie, whose death affected him deeply.
This personal name is distinct from his public authorial name, C.S. Lewis. The initials came from his legal name, while “Jack” belonged to his private and social identity. Lewis’s close circle at Oxford and Cambridge generally knew him as Jack, which is why biographies, letters, and memoirs frequently use that name without treating it as a separate person.