J.K. Rowling added the initial K in honor of her paternal grandmother, Kathleen. Her birth name is Joanne Rowling, so the K is not a second middle name recorded at birth.
When Bloomsbury prepared to publish Harry Potter and the Philosopher’s Stone, the publisher requested initials rather than Rowling’s full first name. The intention was to avoid discouraging boys from reading a book written by a woman. Rowling selected K as a tribute to Kathleen Rowling.
The resulting author name, J.K. Rowling, became internationally recognizable after the success of the Harry Potter series. Rowling has explained that she did not actually have a middle name, despite the widespread assumption that the initials represented “Joanne Kathleen Rowling.”
This naming history is separate from her married surname, Murray, which she used for a period, and from Robert Galbraith, the pseudonym used for her crime fiction. The K refers specifically to Kathleen.