euphemism

Recorded in English since 1656, from Ancient Greek euphēmismós, itself from euphēmízō, built on eúphēmos meaning 'uttering sound of good omen, abstaining from inauspicious words.' That in turn comes from eû, 'well,' plus phḗmē, 'a voice, a prophetic voice, rumor, talk,' from phēmí, 'to speak, say.'

The Greek root was about avoiding ill-omened speech entirely, choosing words carefully so as not to invite bad luck. English borrowed the term in the mid-1600s to name that same habit of softening or disguising blunt truths with gentler words.

It shares its root phēmí, 'to speak, say,' with other English words built on 'phe-' or 'phon-' speech roots, though the facts here don't name a specific cognate to point to.