Alveva, Alviva and Elviva are Latinized forms. (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])Elgiva and Elveve are other forms. (Source: Sheard, K.M., (2011), Llewellyn's Complete Book of Names: For pagans, witches, wiccans, druids, heathens, mages, shamans & independent thinkers of all sorts who are curious about names from every place and time, Llewellyn's Publications, Woodbury, Minnesota, USA, page 195) Alfífa is the Icelandic and Old Norse form. (Source: https://www.nordicnames.de/wiki/Alf%C3%ADfa)
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])
Elgiva and Elveve are other forms.
(Source: Sheard, K.M., (2011), Llewellyn's Complete Book of Names: For pagans, witches, wiccans, druids, heathens, mages, shamans & independent thinkers of all sorts who are curious about names from every place and time, Llewellyn's Publications, Woodbury, Minnesota, USA, page 195)
Alfífa is the Icelandic and Old Norse form.
(Source: https://www.nordicnames.de/wiki/Alf%C3%ADfa)