The “J” in J.K. Rowling’s pen name represents her first name, Joanne.
Rowling was born Joanne Rowling in 1965. She did not originally have a middle name. Her publisher requested two initials for the Harry Potter books because research suggested that books by a female author might appeal less strongly to some boys. Rowling selected K in honor of her paternal grandmother, Kathleen.
The resulting name, J.K. Rowling, became the public name associated with the Harry Potter series. Rowling has also published crime novels under the pseudonym Robert Galbraith, a separate author identity that allowed her to write outside the fantasy market.
The “K” therefore does not represent a birth middle name. It was added as part of the publishing name, while the “J” is directly tied to Joanne, Rowling’s actual first name.