If it were to be anglicized or otherwise modernized, I think it would be spelled Elfiva, Elfyiva, Alfiva, Alfyiva, Alfeva, or Elfeva. But most likely Elfiva, though I do prefer Alfeva. This is based off of Sunniva.
In the seventh scene of The Bayeux Tapestry, a mysterious woman by this name appears to be being struck in the face by a clergyman. No one knows who this woman is or to what the scene refers.
Aelgifu, also known as, Ælfgifu, Alfgifu, Alfgitha or Elfgifu, was a daughter of Ælfhelm, Earl of York, who was murdered on the command of Ethelred the Unready, the King of England.
The name was also given as a royal title to Aethelred's second wife Emma of Normandy (who later married King Cnut) in honour of Aethelred's grandmother St Aelfgifu.
(Source: https://www.s-gabriel.org/names/talan/reaney/reaney.cgi?Alviva)
Alueue/Alveve, Ælueua/Ælveva, Elueua/Elveva,
Eluiue/Elvive, Eluyua/Elvyva, Helueua/Helveva are other forms. (Source: https://heraldry.sca.org/names/reaneyAG.html)
Alvive is another form. (Source: https://anglisc.miraheze.org/wiki/Anglish_Given_Names [Under the "Anglo-Saxon Names" category])
Alfífa is the Icelandic and Old Norse form.
(Source: https://www.nordicnames.de/wiki/Alf%C3%ADfa)