The “K” in J.K. Rowling’s pen name stands for Kathleen.
Rowling was born Joanne Rowling and did not originally have a middle name. Her publisher, Bloomsbury, wanted a name that might appeal to boys as well as girls, so she used initials instead of publishing as Joanne Rowling. Rowling chose “K” in honour of her paternal grandmother, Kathleen Ada Bulgen.
The name is therefore not simply an abbreviation of a middle name given at birth. “J.K. Rowling” became the professional name attached to the Harry Potter novels, while Rowling continued to use Joanne in her personal and legal life. The name’s design was a publishing decision made before the first novel appeared.
A further distinction matters in later bibliography. Rowling published the Cormoran Strike crime novels under the pseudonym Robert Galbraith, rather than under either Joanne Rowling or J.K. Rowling. Her children’s books under the Harry Potter brand retained the J.K. Rowling name.