As for how the dogwood got its name, one explanation is that dog owners once
made a tonic from the bark to wash their pets. A more likely derivation
comes from the Old English term doggerwood, meaning "a stick once used to
skewer meats."

I knew about the legend, but does anyone know any other logical explanation for
the name?
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The tree got its name from its berries, which were called "dogberries" because
they were worthless—"dog" is commonly used among botanists to mean "inferior
quality" or "worthlessness."