The K in J.K. Rowling’s pen name represents Kathleen.
Rowling was born Joanne Rowling in 1965. She did not originally have a middle name, but her publishers asked her to use initials for the Harry Potter books because they believed young male readers might be less likely to choose a book written by a woman. Rowling selected K in honor of her paternal grandmother, Kathleen Ada Bulgen.
The author therefore became J.K. Rowling rather than Joanne K. Rowling in the usual biographical sense. The name was used for the Harry Potter series and became globally associated with the author.
A common mix-up is assuming that the K stands for Rowling’s own legal middle name. It was adopted as part of her publishing name, while Kathleen was her grandmother’s name. Rowling later used other names, including Robert Galbraith, for her crime fiction.