I feel honored by the proposal "Blechschmidt duality", but I fear that if the goal is to have a more contentful name then this would be a step in the wrong direction :-)
Just for fun, let me add a cryptic proposal: "Nullstellensatz."
The classical Nullstellensatz seems to be more precise as it finds solutions in the algebraic closure, while our version leaves the ring in which a solution can be found open.
I feel honored by the proposal "Blechschmidt duality", but I fear that if the goal is to have a more contentful name then this would be a step in the wrong direction :-)
Just for fun, let me add a cryptic proposal: "Nullstellensatz."