The middle name in Joanne Kathleen Rowling is Kathleen.
Rowling was born Joanne Rowling, without a middle name. When her first Harry Potter book was prepared for publication, Bloomsbury wanted her name to appeal broadly to young readers and asked for a second initial. Rowling selected “K” in honor of her paternal grandmother, Kathleen Ada Bulgen.
The resulting author name was J. K. Rowling. The initials helped create a memorable publishing identity, although Rowling has said that she did not actually have a middle name at birth.
This detail is often mixed up with the author’s pen name Robert Galbraith or with the character Harry Potter’s middle name, James. Kathleen belongs to Rowling’s professional name, not to a character in the Harry Potter story.