This would work the same as the regular z-order change commands on objects, but apply to the (temporary or permanent) layer. In fact, you can use those commands for it with a few modifications. Note that they move 1 step up/down relative to the objects that the selected object (or, in your case, layer/group) overlaps; I think this also makes sense to preserve for moving group-layers.
? could you elaborate?
Try it with the regular z-order commands. If you have this z-order:
A B C
and you're moving A one step down, then it checks if the bboxes of A and B overlap. If they do, it puts A under B. If not, it checks the same for C, etc. In other words, z-order commands only consider the stack of objects that bbox-overlap the current object, not the entire z-order stack of the document. (Until I implemented that, one-step z-order changes were almost unusable in big documents.)
Now, with layers, I think it depends on what we're moving relative to what. If you're moving a layer relative to other layers, I don't think you need to check bboxes. However if you're moving a layer relative to sibling objects, you do need to implement the same bbox checks. I think this will be the expected behavior.
Well, the intent is that they will eventually move objects just as you describe. I just haven't implemented that part yet.
OK, then "Move" is appropriate.
I'm still not sure whether we would really need a separate command for simply switching layers or not.
OK, we'll see. That depends on how convenient and keyboard-friendly is the layers widget. If it's just "Shift+Alt+L, Up, Esc" to switch one layer up then indeed we may not need a verb for that.