J.K. Rowling's middle initial was intended to represent Kathleen.
Rowling was born Joanne Rowling and did not originally have a middle name. Before publication, Bloomsbury asked her to use two initials because the publisher believed that a gender-neutral author name might appeal to boys. Rowling chose “K” in honor of her paternal grandmother, Kathleen, creating the pen name J. K. Rowling.
The author has said that her name is pronounced “Joanne Rowling,” rather than “Joanne K. Rowling.” The initial was a publishing name, not evidence that Kathleen was part of her birth name. Her name is also often written without spaces as J.K. Rowling, the form used on most editions and publicity.
The choice belongs to the history of the first Harry Potter publication in Britain. In the United States, the books were marketed under the same author name, although the title of the first novel changed from Philosopher's Stone to Sorcerer's Stone. Rowling later used Robert Galbraith for her crime fiction.