What about a bog garden? Otherwise a key term for you might be "moraine". Depends on how much water, if any, seeps in from the sides, and when - since winter is the wet time in our area a moisture bed may be damp at the wrong times for many plants unless the moisture is trapped and held in place for summer.

To make a sunken rock garden in a wet climate, I'd advise building planted walls around the edges and laying pavers or gravel on the bottom, over some good drainage. The bottom could then be used as a seating area from which to admire the plants growing in the walls, and you would have the advantage of a full range of sun exposures to suit different plants. I saw something like this done very well in western Oregon.