Yes, it does exist. Hope that answers this well-articulated question.
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A polygon with 1000 sides is still a polygon but even a polygon of 100 sides gives characteristics of a circle. When demonstrating circles a polygon of 100 sides helps show the circle characteristics.
While a 100-sided polygon has no official name, the most commonly used terms are "hectogon" and "centagon".
There is no name for it. A magagon has a million sides though. There's one for you.
There are: 0.5*(1002-(3*100)) = 4850 diagonals
A polygon with 6 sides is a hexagon and a polygon with 8 sides is an octagon