The casting call described her as "[DOCTOR] 30s.. male or female, any ethnicity. Working rounds in the E.R. Good bed-side manner. Smart. Knows what’s best for the patient and won’t be questioned or pushed around. CO-STAR."
Although being an unnamed character, the doctor 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".