My husband is in charge of the task of dusting off/cleaning the surfaces being discussed. We have two in our bathroom--one above the sink and one behind the toilet. Plus, there's one in the kitchen, behind the whole section of counter that includes our sink and is below the wall-mounted boiler/water heater. In all cases, they were built to conceal the various plumbing and electrical lines that were added when the kitchen and bath in our 1905-era "Altbau" apartment were finally brought up to modern standards.
He simply says that he's dusted/cleaned/wiped off the "Ablagen."
Of course, that doesn't really address the issue of what the structure underneath the "Ablage" is called...
hm -- us is describing things typically seen in US-style buildings, but the structures being discussed here aren't common in those buildings, for one, I'd say, because construction methods used in those buildings make it easier to conceal plumbing and wiring within the existing wall.
OT: For those who might be working on an automotive translation or similar and have stumbled across this thread, be advised that "Brüstung" has a wide variety extremely diverse uses in the industry, and in some cases, it differs widely between passenger cars and commercial vehicles. Best to ask for an explanation of the specific use of the term from your customer.