A bayberry is one of two plants, a plant of the genus Myrica, a North American shrub with aromatic leather leaves and waxy berries, or a shrub with aromatic leaves which are used in the preparation of bay rum.
Although, all parts of the shrub are used--berries, bark, leaves, and seeds--it is the oil of the seed that is used most commonly today.
To identify shrubs with black berries, look for plants with small, dark berries that grow in clusters. Pay attention to the shape and size of the leaves, as well as the overall growth habit of the shrub. You can also consult a field guide or use a plant identification app to help you accurately identify the shrub.
Lonicera maackii
The black currant shrub is a deciduous with black berries of the Saxifragaceae family.
The name is Holly.
Holly
It sounds like you may be describing a beautyberry shrub (Callicarpa spp.). Beautyberries feature clusters of small, vibrant purple berries that appear in late summer to early fall. They have simple, elliptical leaves and are commonly used in landscaping for their ornamental appeal.
Lycium shrubs typically have thorny branches with small, oblong-shaped leaves. They produce small, tubular flowers that can range in color from pink to purple. The shrub also bears small red berries that are often used for culinary and medicinal purposes.
Sumac
Holly
common dogwood