What is the name of this octagonal shape?

Let's say that this image (imagining that it has eight sides):

is placed on top of this image (an octagonal prism):

What will the resulting shape be called?

It's a heptadecahedron - a 17 sided solid. One of 6,415,851,530,241 topologically distinct convex heptadecahedra.

You don't need to call it an irregular heptadecahedron, as all of them are.

Sorry it's not a very exciting name.

It can be called an "elongated octagonal pyramid." See elongated pyramid on Wikipedia: "the elongated pyramids are an infinite set of polyhedra, constructed by adjoining an n-gonal pyramid to an n-gonal prism."

Of course, you're going to have to explain what you mean if you ever use this term, so its utility is questionable, unless you are referring to such things repeatedly.