The story
Desmo: word-forming element used in scientific compounds and meaning "band, bond, ligament," from Greek desmos "bond, fastening, chain," related to dein "to bind," from PIE root *dē- "to bind." Pressin: from vasopressin, the hormone that desmopressin is an analogue of, that causes increased blood pressure.
Etymology from Wiktionary, CC BY-SA 4.0.