Can anyone identify this Shimano derailleur?
That's Shimano's C050 rear derailleur. It is comparable to Atlus and Tourney in quality and I believe only came as a 7 speed, like yours.
I've attached the technical manual so you can see how to set it up properly. If you're looking to replace it, Shimano provided a lot of high end 7 speed rear mechs. For a mountain bike that would include things like exage, deore lx, and so on. The same time period for road and commuter bicycles would be exage, some rsx.
One fair warning to add to the previous answer. The "C" models from Shimano were Rapid Rise. They don't make this system any more, but it means the cable pull is reversed and when you change this out for a non-rapid rise rear derailleur the shifters will read backwards. This means when they say they are in 8th speed, they will actually be in 1st, and vice versa. Non-rapid rise derailleurs are otherwise compatible with rapid rise shifters, and the shift points should all match up and work fine. If you want the shifters to read correctly, you should change the shifters too.