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Peonies don't appreciate competition. If you keep it clear of grass and weeds, give it a bit of gentle fertilizer, and keep it watered, it should reward you with blooms.
As for IDing the peony, unless it is very distinctive in the appearance of it's mature foliage and/or flower, it is unlikely. There are a lot of cultivars and they are often times very similar in color and form. Most of us own unidentified plants and enjoy their many charms, ID'd or not.
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