The “K” in J.K. Rowling’s professional name represents Kathleen.
Rowling was born Joanne Rowling and did not originally have a middle name. Her publisher asked her to use two initials because research suggested that some young boys might be less likely to read a book written by a woman. Rowling chose “K” from Kathleen, the name of her paternal grandmother.
The author’s name is therefore usually written as J. K. Rowling, with spaces and full stops in the British style. The name is a pen name rather than a complete expansion of her birth name. She has also written crime novels under the separate pseudonym Robert Galbraith.
A common mix-up is to assume that the K stands for Rowling’s own middle name. It does not: Kathleen was selected in tribute to her grandmother. Rowling’s legal name changed after marriage, but her best-known publishing name remained J.K. Rowling.