With a body of revolution we take a curve and repeat it about a circular path. There is nothing that prevents us following a non-circular path as shown in the two images below. Of course, this requires stretching (or contracting) the curve as required to meet the boundary conditions on the generating curve.
A further extension of the idea is to morph the generating curve as it traverses the planiform curves-as long as it returns to the original shape after a rotation of $2\pi$ radians. Yet another idea, for toroid-like volumes, is to rotate the generating curve (a closed curve) as it revolves about the toroid axis. These have all been demonstrated.
I was wondering if there is an specific name these kinds of volumes.
