J.K. Rowling’s surname before she married Neil Murray was Rowling.
She was born Joanne Rowling, so “Rowling” was her family name from birth. She later used the name Joanne Rowling professionally, although her books were published as J.K. Rowling. The initial “K” was added for the pen name at her publisher’s suggestion; Rowling did not have a middle name at birth, and the K refers to Kathleen, the name of her paternal grandmother.
Rowling married Neil Murray in 2001. After that marriage she could use the surname Murray privately, but her established author name remained J.K. Rowling. She has also published crime novels under the separate pseudonym Robert Galbraith.
This question is easily confused by the number of names associated with the author: Joanne Rowling is her birth name, J.K. Rowling is her principal author name, and Robert Galbraith is her crime-fiction pen name. “Murray” is her married surname, not the surname she was born with.