I'm trying to imagine how we would specify this, given how many different ways there are to dump objects. I usually control the dwarves' dump behavior by disabling all the other garbage dumps than the one I want the dwarves to use. But, that means I usually only have one dump zone active at a time. If the objects "remembered" which dump zone(s) was/were active when the dump designation was made, then I could switch my dump zones back to "normal" even if I am doing a specialized dump with some other objects at the same time.
On the other hand, sometimes you would want previously-designated objects to be directed to a freshly-activated garbage dump, so there should be a way to do that. Maybe that should be an option in the o menu, or perhaps you would achieve that by completely deleting the garbage dump you no longer want to dump into. Or, maybe there would just be an option when inspecting the garbage pile to redirect all the objects that currently want to dump into it. Of course you could always un-dump and re-dump the objects but that might be a hassle.
It would be nice if you could inspect an object and have the game tell you where the dwarves are planning to take it. But, this would be great to have not only for objects marked for dumping, but also for objects that have been chosen to place into a stockpile.
One final thought: it would really help to manage your garbage dumps if we had a list somewhere. Maybe this is already in the development branch, since rooms and locations are currently undergoing major changes.