Seems highly likely. "hyrst" is specifically a wooded hillock or knoll as opposed to a "den" - a wooded valley etc
Ring is from "hring" meaning a circle but can sometimes be from "Hring" a personal name. There are similar place names like Ringstead, Ringwood, Ringmere etc. Unfortunately "ring" can be also derived from "rima" a border or "hringe" a salt pan.

The"stain" element seems the most certain as it always derives from "stan" and putting all three elements together, you seem to have a stone circle on a wooded hillock. Hope you find It!