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They are referred to as [bedroom reading lamps.](http://www.pegasuslighting.com/led-adjustable-reading-lights-headboard-mount-3w.html?utm_source=googleshopping&utm_medium=cpc&utm_term=PBL3SC-WW-NK&utm_campaign=googleshopping&CAWELAID=1665494158&CAGPSPN=pla&catargetid=400007360000074928&cadevice=c&gclid=CjwKEAjwndqrBRC16IyeqPicp3ASJAB-vB-c7yKdzlewqHfODWlwcmrKWAKTAf9zqvP3GkzzyexW5hoCaLvw_wcB) You should find them on Google as wall-mount reading lamps. Also called Gooseneck spot light. There seems to be a lot of different names for it.