The first name represented by the J in J.K. Rowling is Joanne.
Rowling was born Joanne Rowling in 1965. She did not originally have a middle name, but her publisher asked for a name made from initials because research suggested that some young boys might be less likely to choose a book by a woman author. Rowling selected K for Kathleen, the name of her paternal grandmother, creating the author name J.K. Rowling.
The initials are therefore not a shortened form of two given names she received at birth. Rowling has also been known as Joanne Murray during her marriage to Neil Murray, but her books have generally appeared under J.K. Rowling. The initial-based name became one of the most recognizable author identities in modern publishing, while the author later used Robert Galbraith for her crime novels.