What is a three-dimensional hexagon called?

Answer 1

There is no such thing as a 3-D hexagon.

A regular hexagon will tessellate and so it forms a plane (2-D) surface, not a 3-D shape. A 3-D shape with six faces is a hexahedron and this could be a triangular bipyramid, a parallelepiped or a pentagonal pyramid.

Answer 2

A three dimensional hexagon is can be called a hexagonal prism. This is similar to a cylinder, except on each end, instead of a circle there are hexagons.