What is the niche in the wall for the bed called?
Such a niche
called an "alcove". A niche that is made specifically for a bed, by the way, is a very convenient and practical invention.
The niche in the wall for the bed is called an alcove. This is a small makeshift bedroom, or, more simply, a secluded corner for relaxing in a room where there is no bedroom as such. Alcove in Arabic means a tent, a depression, a niche.