We can work with unnameable things very easily. Take, for instance, every known theorem that quantifies over all real numbers. If you try to argue that proving theorems about these real numbers does not constitute “working with” them, it seems you have chosen a rather deficient definition of “working with” that does not match with how that phrase is used in the real world.

I would argue that all of those theorems work with nameable sets of real numbers but not with any unnamable real numbers themselves.