Is there a common name for the surface z = xy?

Question

I would call it a saddle, but it's not the standard saddle. Is there a standard name for it, the way we have 'hyperboloid of one sheet' for example?

Answer 1

It's called "the saddle" :). Substitute $x=(u+v)$ and $y=(u−v)$ to get $z=(u+v)(u−v)=u^2−v^2$, which is a more conventional parametrization of the surface, while the surface itself is unchanged.