If the metal ring is at the far end of the handle it's known as a "hoop". If it's on the end closest to the metal part of the chisel, it's known as a "ferrule". I don't like hoops and don't think they're necessary (except maybe on Japanese chisels - and even then I don't like them). The hoop is there so that when you beat the hell out of your chisel, the hoop keeps the wood handle from splitting. But you don't normally beat a chisel that much. Old mortise chisels, known as pigstickers, do not have a hoop on them and they are beat pretty hard. If you hit your chisel with a wooden mallet you won't beat up the end of your chisel handle very much - or it will take you a long time to mushroom them badly.
The reason I don't like hoops is because when I use the chisel in push mode, the hoop and the rough end of the handle are not comfortable in my hand. I have a set of Japanese chisels and I rehandled them with western type handles. (Japanese chisels are traditionally hit with a metal hammer so the end of the chisel handle gets mushroomed pretty badly - I hit mine with a wooden mallet.)
Also, it's very easy to make chisel handles so if you do bung up the end of your chisel handle it's easy to make a new handle.
If you're referring to the ferrule, that is necessary and does not cause any problems with the handling of the chisel.
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