What is the surgery proceedure to remove stenosis in the left carotid artery where it comes out at the top of the aorta?

There are several: If you mean a stenosis in the common carotid off the aorta, the procedure would either be a stent or a carotid (or innominate) endarterectomy. Much more common is a carotid endarterecomy, however this occurs where the internal carotid comes off the common carotid, not the aorta.

Several options: Assuming the left subclavian artery doesn't have any blockage, a bypass from this vessel to the left carotid, a subclavian-carotid bypass, is the best surgical approach. This can be done with a small incision in the lower neck. Another option is a carotid angioplasty and stent, which can be performed from the femoral approach, or retrograde, via a small incision in the neck.