The middle initial in J.K. Rowling’s author name is K.
Rowling was born Joanne Rowling, without a middle name. When Bloomsbury prepared to publish Harry Potter and the Philosopher’s Stone, the publisher asked her to use initials rather than her full first name. The intention was to make the book appealing to a broad audience, including readers who might be less likely to choose a book by a woman.
The K stands for Kathleen, the name of Rowling’s paternal grandmother. “J.K. Rowling” therefore combines her first initial with a family name that was added for her publishing identity rather than being part of her birth name.
She later used other names for different kinds of writing. The Harry Potter novels carry J.K. Rowling, while the Strike crime novels were initially published under Robert Galbraith. The initial is consequently a specific part of her author branding, not evidence that Kathleen was her own first name.