What are the names for a light-duty hoist/pulley system components?
You could search for something called a block and tackle. This is a rope and multiple pulley system that gives you a mechanical advantage over a single pulley making it much easier to hoist the tire into place. 

You should consider mounting four hooks on the ceiling overhead so that the block and tackle can be moved to the position where the tire will be resting on the shelf. The upper "hook" could even be a bar or pipe affixed to the ceiling in such manner that the top securing point for the block and tackle can be slid back and forth so that it can be pushed into position before hoisting each tire.