Variant spelling of Gavin/Gawain, from Welsh meaning 'white hawk'; an Arthurian chivalric name.
Gavyne is a variant spelling of Gavin or Gawain, from Welsh roots meaning white hawk. That puts it near the Arthurian world, where the name gains chivalric and literary associations through the figure of Sir Gawain.
The spelling Gavyne gives the old material a more stylized, contemporary look. It still feels noble and mythic, but with a softer visual texture than the more standard forms. The result is a name that combines bird imagery, medieval romance, and modern customization.