The “K” in J.K. Rowling’s professional name is said to represent Kathleen.
Rowling was born Joanne Rowling and did not originally have a middle name. Her publisher asked her to use two initials for the Harry Potter books, partly because a gender-neutral author name was thought to appeal to young readers. She chose K for Kathleen, the name of her paternal grandmother.
This means J.K. is not a conventional expansion of Rowling’s birth name. Rowling has also been publicly known as Joanne Murray during her marriage to Neil Murray, but she continued writing under J.K. Rowling. The initials became one of the most recognizable author brands in modern publishing.