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, dag (v.) "to pierce or stab" (1630s, perhaps 15c.) -- the trees have hard, white wood that was used in making skewers; another name for it was skewer-wood. But another guess is that the tree was given the name in reference to its fruit, which was called dogberry from 1550s, and dog had implications of "cheap, inferior" (i.e. "fit for a dog").