J.K. Rowling used the initials J.K. on the covers of the Harry Potter books.
Her name at birth was Joanne Rowling, so the “J” comes from Joanne. Rowling has no middle name beginning with K. Her publishers requested a name made from two initials before the first Harry Potter novel was published, because they thought a gender-neutral author name might appeal more broadly to young readers, especially boys.
Rowling chose “K” in honour of her paternal grandmother, Kathleen. She therefore became known professionally as J.K. Rowling, even though “K” was not part of her original given name. In later life she has also published under the name Robert Galbraith for her crime novels.
The initials are sometimes mistaken for an abbreviation of a longer formal name. They are instead a publishing name built from Joanne and Kathleen. Rowling has also used the name Joanne Murray following her marriage to Neil Murray, but her best-known author name remains J.K. Rowling.