I think the most common name would be "steam jet refrigeration" From My understanding it was used a lot in the 1930s for theater AC systems. Any place that had a boiler, could use the steam to cool as well.
As to the efficiency, any time you can use heat in it's native form to do your work, you have saved several inefficient steps.
I also found this better link.
I think the main issue with this technology, was that it did not scale well.
Another thing to look at for reference only is how airlines chill the cabin air.
Comperssion(in the jet engine), radiate the heat to the outside, and expand into the cabin(with those little nozzles over the seats.)