When you go to a doctor and explain health problems that you have, the doctor "diagnoses" you. That means that the doctor tells you the name of the illness that you have.
You can say which illness or disease a person has with the phrase "diagnose ___ with ___":
They diagnosed me with a rare blood disease.
"Diagnose" is a scientific technical-sounding word. It would seem strange to say something like "The doctor diagnosed me with a cold" because "a cold" is not scientific or technical.