A pentagonal heptahedron is a heptahedron comprising two pentagons which are joined to one another by five quadrilaterals. There is no requirement for the pentagons to be congruent nor for them to be parallel to one another.
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A hexagonal based pyramid is the best description since it is not ambiguous. The shape is a heptahedron but that name could also apply to a pentagonal prism as well as some exotic shapes.
A polyhedron of 5 or more sides can always be found that has a rectangular face. So three shapes are:a pentahedron (rectangle based pyramid),a hexahedron (cuboid),a heptahedron (pentagonal pyramid).
heptahedron
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A pentagonal what? A pentagonal pyramid or pentagonal prism have different numbers of vertices.