C.S. Lewis’s surname was Lewis; N.W. Clerk was a pen name rather than an earlier surname.
Lewis used the pseudonym N.W. Clerk for All My Road Before Me, a published selection from his diaries. The initials and name helped present the material at some distance from his better-known public identity. The book records Lewis’s life during the years surrounding his undergraduate studies and early academic development.
His full birth name was Clive Staples Lewis. He became known publicly by his initials, C.S. Lewis, rather than by the childhood nickname “Jack” that he adopted for himself. N.W. Clerk therefore does not represent a family name or a legal change of surname.
This fact is easy to muddle with Lewis’s other names. “Jack” was his preferred personal name, while “C.S. Lewis” was his authorial identity. N.W. Clerk was a literary pseudonym used for a particular diary-related publication.