Spelling varies depending on the audience and usage. Generally speaking: Use orthopedic(s) for patient audiences or general external audiences; use orthopedic surgery for academic or physician audiences. Also, please note the following:
The name of the department is Department of Orthopaedic Surgery.
The name of the clinical service practice is Washington University Orthopedics. The clinical service line is orthopedics.
Faculty members are professors of orthopaedic surgery.