A lot of writers choose to represent themselves with initials instead of given names. Such as E.E. cummings. T.S. Eliot. And J.K. Rowling – in the case of the Potter scribe.
However, the “K” doesn’t really stand for anything. Joanna Rowling has no middle name, but her publisher thought Harry Potter would be selling better if she disguised her gender.
Thus, the mysterious “K” was born, which Rowling attributes to “Kathleen”, her grandmother.