There is no specific name for such shapes.
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There are infinitely many of them so it is not possible to name each one. Collectively, they are polygons.
Octagon, dodecagon, myriagon.
A shape with more than 10 sides may be called a polygon - but only if all the sides are straight lines - and there is nothing in the question to suggest that they are.
There is no special name that distinguishes shapes with more than four sides from shapes with four or fewer.
Shapes having less than 4 sides or more than 4 sides are not parallelograms
There is no specific term that distinguished between shapes with more than 11 sides from those with up to 11 sides.