Modern invented name; possibly bird-like or from the river Avon.
Avyn is a contemporary American coinage without a singular ancient root. It is often interpreted as a creative variation of the Welsh name Evan or the Celtic word 'Afon' meaning river, while its sound also evokes the Latin 'avis' for bird.
Less common today
Avyn isn't in the latest US Top 1000. It last peaked at #4,753 in 2013.
US births per 5-year period, 1990βpresent (SSA data).