You have a hydrangea shrub with a lacecap type blossom. I believe it is a hydrangea serrata, there is a small one called Tuff Stuff. It's blossoms aren't necessarily white, but many hydrangeas start out white then develop color as the season progresses. Lanarth is a variety that stays more white in at least the larger flowers around the edges, is reported to grow to three feet but could stay smaller under some conditions. If your plant stays white it is Lanarth.