What are some common symptoms of having a heart murmur?

It depends. If it is an innocent murmur, there are no symptoms, as there is no problem. If the murmur represents a heart problem, the usual symptoms of chest pain, shortness of breath, palpitations, exercise intolerance, etc, all apply.
Heart murmur. The symptom of heart murmur depends on whether the murmur is physiological or pathological.Most of the time you have no symptoms but murmur can cause various symptoms like palpitation, chest pain, tiredness and fatigue, shortness of breath, sweating, syncopy, abdominal swelling and at times it can also cause hemoptysis.