The story
From swallow + wort, because the plant's parts were traditionally fancied as resembling a swallow's tail. Compare celandine.
Etymology from Wiktionary, CC BY-SA 4.0.
swallow-wort
Today it means: The plants of the genus Vincetoxicum, especially Vincetoxicum nigrum (syn. Cynanchum nigrum, black swallow-wort) or (Vincetoxicum hirundinaria (syn. Cynanchum vincetoxicum, white swallowwort). Full definition →