Tartessian Aiburis (updated)

Tartessian aibᵘuris /Aiburis/ appears at the beginning of a funerary inscription (J.3.1) and is frequently interpreted as an anthroponym whose second element -ris would correspond to Celtic *-rīxs 'king' > -rix, which in fact is the most frequent element in Gaulish anthroponymy¹. However, the first element aibu- (likely reflected in Iberian aibe), doesn't have a clear Celtic etymology, although it appears in the Gallaecian theonym Aebosocelensis² and possibly also the toponym Aipora (modern Évora)³.

Prósper proposes a link to Greek aipús 'steep, craggy', aípos 'hill, crag', whose etymology is disputed⁴. If the labial stop comes from a labiovelar, we could compare it to the Italic toponyms Aequāna, Aequum Faliscum and Aequimelium (a village on the hillside of the Capitoline), the latter being a calque of the Gallaecian form. Although homonymous to Latin aequus 'equal; fair, even' < *aikʷo-, we can hardly expect Aequimelium to mean 'confraternity hill' or the like.

On the other hand, we've got Gallic (Gaulish) *aikʷo-randā 'boundary' as the source of the toponyms Aigurande, Eguérande, Eygurande, Iguerande, Ingrande(s), Yvrande(s), La Guirande, Eurande, etc⁵. The first element *ekwo- has been alternatively linked to Latin aqua 'water' (absent from Celtic) or aequus, but in my humble opinion it would make more sense to be a foreign loanword related to the Italic toponyms. 

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¹ X. Delamarre (2008): Dictionnaire de la langue gauloise, 2nd edition, pp. 259-260.
² B.Mª. Prósper (2000): Lenguas y religiones prerromanas del occidente de la Península Ibérica, p. 112.

³ J.T. Koch (2013): Celtic in the South-west at the Dawn of History, 2nd edition, p. 141.
⁴ P. Chantraine (1968): Dictionnaire étymologique de la langue grecque, p. 37-38.

⁵ X. Delamarre, op. cit., pp. 163-164.