Common Bluebeard is a small shrub native to eastern Asia and grown in some U.S. gardens. Blue to purple flowers form separate clusters around the upper stems. In U.S. gardens, the name bluebeard often refers to the related bluebeard garden hybrid (Caryopteris × clandonensis).
Common Bluebeard usually has obvious teeth along its leaves. The garden hybrid varies by cultivar and can also have toothed leaves, so a flower photo alone may not settle the ID.
Why they get mixed upThe hybrid has blue flowers and is a cultivated descendant of this species.