Private health service plans which promise to provide care, not merely pay for it, are often referred to as Health Maintenance Organizations or HMO's. Some are "closed panel plans" and operate out of a central facility, with all the health care providers employed by the HMO. When you go to the facility you may see the doctor on duty, or your "assigned physician".
Other HMOs are more loosely affiliated models, sometimes called Individual Practice Associations, where the participating health care providers operate from their own offices.