Æðelgifu

Athelgifu and Ethelgifu are other forms.

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Sources: https://thehistoryofengland.co.uk/blog/podcast/2-5-life-on-the-inland/
https://www.umastro.com/babynames/meaning-of-Ethelgifu

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Ethelgiva is a younger form.

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Source: https://freepages.rootsweb.com/~fesschequy/genealogy/EightWessexSaints.html

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Atheliva could be a modern form.
Source: https://oswinkinsey.wordpress.com/ (See the document called "English Compound Names" by Oswin Kinsey. "Atheliva" is on page 112.)

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Ellive could be considered to be a modern form. Source: https://anglisc.miraheze.org/wiki/Anglish_Given_Names ('Ellive' is under the "Anglo-Saxon Names" category)

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Aelive, Aileua/Aileva, Ailiue/Ailive, Ailiva, Aliua/Aliva, Alyva, Ayliua/Ayliva, Æileua/Æileva, Eileua/Eileva, Eileue/Eileve, Eilieua/Eilieva, Eilliva and Eleua/Eleva are other forms. Source: https://heraldry.sca.org/names/reaneyAG.html

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Elgiva and Aileve 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