The name said to be derived from the Irish word for "vine" in this site's dictionary is spelled
Fíona, not
Fióna.
The form "
Fióna" is "user-submitted" and is said to be the Faroese form of
Fíona or
Fiona, not an Irish or Gaelic form.
So you would seem to be incorrect in your original statement that this site claims that the Irish Gaelic form
Fióna is derived from the word meaning "vine".