There is not a name for such a polygon. A polygon with one million sides is called a megagon though..
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I don't know the exact amount when it starts, but I just tried it with 1 trillion sides and each angle was 180. So we know it starts between 1 billion and 1 trillion sides.
Polygons can't have curved sides so the answer is not a polygon.
trapazoid
While there is no prevalent name for such a polygon, due to its insurmountable number of sides (to the unaided eye, it would be indistinguishable from a circle; such a polygon would still be indistinguishable from a circle if it were the same size as the sun, and would need to be several lightyears in diameter before its angles would be discernible and its perimeter of significant distance from that of a corresponding circle). A term can be inferred from the metric naming system: 1 billion is represented by 'giga', ten by 'deca', so an approximate name would be 'decagigagon'.
360/1 = 360 sides