I've been trying to figure out the name for this element but I've been having trouble finding it. It should snap in three locations: to the top of the screen, to the bottom of the screen, and a 5th of the way up from the bottom of the screen. The window should be draggable as noted by the three lines.
It's a splitter and pane…
The draggable control itself is a splitter, of one kind or another. The separate space that is created by dragging the splitter usually called a pane or sometimes a panel. To confirm that this is the kind of interaction you meant to describe, have a look at these samples: Telerik example or DevExpress example. There are other samples out there, of course.
…or perhaps not
This interaction is less likely to be called a drawer or an accordion section. It all depends on how this interaction is implemented.