"the berry of the dogwood tree," 1550s; see dogwood + berry.
Entries linking to dogberry
dogwood n.
shrubs and small trees of the genus Cornus, 1610s, earlier dog-tree (1540s); the first element sometimes said to have been perhaps dag — compare dagger and dag (v.) "to pierce or stab" (1630s, perhaps 15c.).
The trees have hard, white wood that was said to have been used in making butchers' skewers; another name for it was skewer-wood. This explanation is as old as the word itself in English, but the form *dagwood is not attested. Another guess is that the tree was given the name in reference to its fruit, which was called dogberry from 1550s, and dog (n.) had implications of "cheap, inferior" (i.e. "fit for a dog").
berry n.
Old English berie "berry, grape," from Proto-Germanic *basjom (source also of Old Norse ber, Middle Dutch bere, German Beere "berry;" Old Saxon winberi, Gothic weinabasi "grape"), which is of unknown origin. This and apple are the only native fruit names.