Do you mean eidos? Eydos would be rendered eudos but eidos means 'that which is seen; form, shape' and you're making a major leap from Alea to Al-. Etymology is never guess-work, not when done properly. It's based on evidence gleaned from records and writing and only when incomplete but all other possibilities have been all but eliminated do you get that 'most probable meaning' bit. Were other pre-Hellenic gods used in personal naming? Was the form of contracting from Alea to Al- usual or documented elsewhere or was Ale- or Alea- the normal pattern? On that sort of evidence you might find some basis for 'form of Alea'...though why on earth the Greeks, given their naming practices, would go for such theological cheek and ambiguity is beyond me.
If you want guesswork from a Greek stance it's rather easy...there's aleiphas ('blotting out, erasure'), Aleias ('flour;), Aleisos ('cup, goblet') and closest and best of all Aleites ('sinner'). But none of these exist as documented personal names, only words and none survived the classical period to lead to a name bestowed today (although a parent learned in Greek could certainly bestow a Greek word as a name today the etymology of the name would then be '21st C. name, English/American, taken from the Greek word aleisos 'cup, goblet' because it doesn't exist as a pattern of naming from Greek times)
Given that you've found it used in Catalan then I'd be looking there - sourcing from Latin/Spanish and Basque. In Latin you have Aleonis ('gambler' Alea in Latin means 'gambling, dice'), Alidus/Aliudus ('other, different'), Alitus ('to nourish; to increase' - great potential that one has) and Altus ('high, deep; profound'). Basque, of course, is an entity unto itself.
The only origin I've ever seen *documented* for Aleydis is Dutch, contracted form of the medieval Adalheidis, from the German Adelaide. That such a name would travel through France to the Basque/Catalan region seems entirely plausible, though a good dig through Basque naming would certainly be an area for research if you're up for such a thing ;o)