The official name of this campus is Washington University Medical Center.
Medical Campus is acceptable only in the context of discussing other Washington University campuses. (Examples: Flu shots will be available on the Danforth Campus and the Medical Campus. Washington University has five campuses: Danforth Campus, Medical Campus, North Campus, South Campus and West Campus.)
Use School of Medicine when the topic involves the school only. (Example: A reception for graduates will take place at Washington University School of Medicine in St. Louis.) Use Washington University Medical Center when the topic involves medical center affiliated institutions. (Examples: Once completed, the highway construction will improve access to Washington University Medical Center.)