Are you diagnosed with heart damage if you've ever had an mi?

Usually. How much heart damage depends on how big of an mi, i.e. How much of the heart muscle lost its oxygenated blood supply due to the blockage in the coronary artery.
Definition of damage. Mi is just one cause of damage. Long term hypertension causes thickening of the heart and is probably most common form of heart disease. High colesterol, smoking, diabetes over time can cause damage to the heart vessels and their funtion. Infections, chemotherapy, radiation, autoimmune diseases, injuries, severe malnutition, excessive alcohol are other causes of "damage" stay well..& good luck.