It looks like the beautyberry or Callicarpa. The berries turn a brilliant, metallic purple in the fall and persist during the winter until the birds gobble them up. They grow on a graceful shrub with arching branches but to keep the most berries coming you will need to prune back a third of the old growth in late winter. This encourages new spring growth followed by more flowers and berries. There are several varieties sold at nurseries and garden centers in the fall when the shrub it most colorful. Keep growing, Marianne Binetti