> There's Levin's complete one way function [1; Section 4.3]. Breaking it is proven to be as hard as any other one-way function, in other words if there exist one-way functions then this is one of them.

So you could refer to Levin's complete OWF as "one-way-function-inversion-complete"? And, since one-way functions are, by construction, the hardest to invert, it's function-inversion-complete?

Edit: Wait, I guess the second part wouldn't follow, because OWFs only include functions that are easy in the forward direction, so they don't necessarily cover functions that are hard in both directions.