Dulcamara means bittersweet which is another name for the plant. When first taken the stems are bitter followed by a sensation of sweetness. Also known as felonwort, originating in the plant's effectiveness in curing abscesses, which were at one time commonly known as felons; the bright red berries are reputed to remove warts and in herbalism today they are used to treat skin conditions.
According to 'Herbal Magick' by Paul Beyerl - Woody nightshade is associated with balancing energies, is harmless and its benevolent properties remain known today - as opposed to its cousin Atropa belladonna (Deadly nightshade) which is poisonous. Having done some further research, however, I do not think this is the case. Other reliable sources clearly state that Woody nightshade is poisonous to humans and livestock though not to birds.
As well as bittersweet and felonwart, other country names for the Woody nightshade are poison flower, shady night, snakeflower, scarlet berry, blue bindweed, trailing nightshade and witch flower.
In the language of flowers Woody nightshade bears the sentiment Truth.