What is the top of a cone called?

Answer 1

The top of a cone, seen from the outside of the cone, is called the vertex, also referred to as the externalpoint.

The vertex is the point of intersection of the lines, or generators, of the cone and the plane base, in this case a circle. But if you just call it the point, everyone will know what you mean.

This is referring to what we all think of when we hear the term, cone: a right circular cone. There are other types of cone, but probably not of interest here.