The J in J.K. Rowling represents Joanne.
Rowling was born Joanne Rowling, and she did not originally have a middle name. Her publisher asked her to use two initials for the Harry Potter books, partly because the marketing team thought a gender-neutral author name might appeal to boys as well as girls.
Rowling selected the second initial K in honour of her paternal grandmother, Kathleen. This produced the author name J.K. Rowling, which became internationally associated with the Harry Potter series.
The author has also used other names. She published the Cormoran Strike crime novels as Robert Galbraith and later wrote the children’s book The Ickabog under her own name. The initials should not be confused with a formal two-part birth name: “K” was added for publishing purposes, while Joanne is her first name.