What diagnosis are covered by insurance to have an echocardiogram?

Many, many, many. The list is too long to write here. Common indications are chest pain, shortness of breath, heart murmur, and abnormal chest x-ray or ekg.
Many -- This is a curious question? You should not have to concern yourself about the diagnosis approvable -- that is your cardiologist responsibility -- but if you have a concern about your heart, then you should see a cardiologist and get your question and concern answered -.