Is there a name for generalized ellipsoids?

Question

In two dimensions, we have the following series of generalizations:
circle $\rightarrow$ ellipse $\rightarrow$ smooth, convex, closed curve $\rightarrow$ smooth, simple, closed curve

And in three dimensions, we could analogously say:
sphere $\rightarrow$ ellipsoid $\rightarrow$ smooth, convex, closed surface $\rightarrow$ smooth, closed surface

(I'm taking the definition of a surface to disallow self-intersection.)

Is there a more concise way I can say "smooth, convex, closed surface"? If one's definition of a manifold includes smoothness, I could say "convex, closed 2-manifold," but that's hardly an improvement.

Answer 1

Use "oval" or "ovoid" for such curves and surfaces respectively. Make sure to provide your own definition for these words though.

Answer 2

I had seen usage of terms oblate/ prolate ovaloids in American literature.