What are the mounts called that can hold a desktop computer on the back of an lcd monitor?

Added (1). but an actual full size desktop. We have them at work and someone asked me to remove it so they can unplug a wire in the back of the computer that is otherwise inaccessible.

Added (2). The link is a picture of an example but that's a mini computer.

Added (3). Here's a better picture -- http://accessories.us.dell.com/sna/productdetail.aspx?c=us&l=en&s=gen&sku=a7023615#Overview

For some reason they have the computer installed in the wrong direction where the back ports are blocked by the base of the stand.

It's because it makes the monitor "mounted" or elevated.

Back of monitor has a "VESA" standard bolt pattern for wall or stand mounting. The extra part that holds the box of the CPU computer is nothing more than a bracket or shelf.
The reason this is so hard to find, is because there are so many varieties of cases and monitors, and so little demand to do what you want. No incentive to make and stock and market this low volume of parts.
Some micro ATX computer boxes (8x8x5 inches) come with one side that has a VESA bracket on it. My city's senior center computer lab has those.
The reason the panel with the connectors is blocked by the stand is to keep people from fooling with the wires.