A word like 'moon' is always a good candidate to reconstruct for a Proto-Language, as it's part of the basic vocabulary of a language. Therefore we should not be surprised to find this word in Proto-Berber. Slightly more surprising though, is the difficulty of reconstruction that really only presents itself now that we have access to Zénaga.
Below is a sample of cognate that I collected for my Master thesis:
Kb. aggur,agur (wa-) pl. agguren, aguren (wa-) `id.'; MA agʷur, ayur (u-/wa-) pl.
agʷurn,ayurn `id.';Tashl. ayyur (wa-) pl. irn (yi-) `id.'; Ouar. yur (u-, wi-) pl.
iyaren `id.';Mzab yur (u-) pl. iyaren `new moon'; Ghd. ōyăr pl. oyărāwăn, end-
oyăr `moon, lunar month'; Aujila ayûr `new moon'; Elfoqaha ayûr `id.'; Zng.
äʔž(ž)ər pl. īž(ž)ärän `moon'; To. ăyor pl. orăn `id.'
First thing you would noticed is that Zénaga has a glottal stop, which you would instantly be inclined to reconstruct for Proto-Berber. The reflex of an indetermined length ž(ž) for *y after *ʔ is regular. This same reflex of *y is also found after *β (cf. *aβăyaw 'grand child' > Zng. āž(ž)uh.
The fascinating part is that this *ʔ clearly isn't there in the plural of Zénaga, the lengthened vowel rather points to an initial *β. So now we're stuck with two consonants as initial consonants that both don't usually show up in other Berber languages. So, let's see if we can find some peripheral proof for either.
The only 'proof' we can find for *ʔ is the initial o in Ghadamès which usually points to a sequence *aʔ, but this is problematic as the original vowel shape of the noun was a-u which is usually reflected in Ghadamès as o-ə (cf. *afuʔs 'hand' Ghd. ofəs 'id.'), this is therefore not very convincing. The ă is coloring of *ə before r.
But if we look for proof of *β in other languages we are considerably more succesful. The languages of interest are Tashelhiyt and Touareg which both have wildly irregular looking plurals irn and orăn respectively.
Believe it or not, these two words doubtlessly point to an identical reconstruction, the problem is that this reconstruction doesn't look very convincing as a plural formation.
The correspondence of Touareg o < *u and i in Tashelhit suggest that this is the previously discussed shift of *eβ > i in Tashelhiyt and other northern Berber languages, u in Zénatic and Touareg.
So that would suggest a Proto-Berber *eβyerăn with a reduced vowel in the État Libre, which is not expected nor probable. And even *aβyerăn would look very odd, it is not usual to replace an u in the singular with schwa in the plural (*a is the usual candidate).
Maarten Kossmann agreed that such a reconstruction was problematic and suggest something different.
For Touareg he suggests *iyorăn > *yyorăn > orăn with loss of initial *y like in the 3sg of the verb, but this loss is only found in Mali Touareg.
For Tashelhit the explanation is more acceptable: He suggest *iβyuran > *iyyuran > *iyyran > *iran with loss of *u which is regular in< triradical roots with the plural suffix *-an. The problem is the plural suffix isn't -an but -ăn, so we must assume that the unattested suffix was original and then was analogicaly replaced with the slightly more common -ăn.
So in the end both these solutions bring a long quite a few more problems, but you would hardly want to consider the form I suggested first which does perfectly explain the forms we find.
An interesting thing to mention is that Ghadamès does not preserve the *β in this position, similar to how *aβwal 'speech' is found as Ghd. awal. Usually the *β is preserved in Ghadamès as β. But apparently directly before a y or w, this consonant is lost.
Heath in his Mali Touareg dictionary connects this word with the root WR 'to rise' which is probably correct. This sadly doesn't help much, as there are no formals that retain the β in Touareg in this root, and Zénaga doesn't seem to have this root either.
Heath mentions the original root to be *whr, but this probably is the Prassian interpretation, which is completely based on internal reconstruction and probably, often, isn't correct anymore.