I have always referred to them as lock rings and the Craftsman version works pretty well on them. ...that is where I got the name because Sears refers to them as long ring pliers.
I have found with those old lock rings the really don't have much spring in them left. I usually find this in floor jacks. I suppose you can replace them with an e-clip or snap ring but I usually throw the old ones on there and use a channellock or my knipex cobras to bend the clip back onto the shaft it belongs. The problem with new e-clips or snap rings is they always seem to be thinner than the original lock rings.