This Nurse worked at the Santa Rosa Mental Health Institute in which Hurley and Libby were institutionalized as patients. When Hurley came back (after being released) to visit Leonard, the nurse would not allow Hurley to see him, as he didn't know Leonard's last name. Eventually Hurley was let in by Dr. Curtis.
Although being an unnamed character, the nurse is in fact named, as her name is shown on her staff badge. However, her name is unidentifiable in the episode. Therefore, she is considered as an "unnamed character".