This bed moves up and down on the wall, and ive been searching all over for what it is called, because i really want it but i cant find it.
There is (or was) a bed that folded up vertically into the wall. It was called a Murphy bed. But the ones in your link rise and descend on a vertical track. The people who make it call it a mobile bed - I think you may be stuck with that unless/until they become popular and get some nickname like hover bed. Added: yes, elevator bed would work.
It's an elevator bed. There are various kinds.
