This is a really interesting question from a phonological perspective. So, while I can't definitively answer the question, I will attempt to shine some light on the subject. It's possible of course that someone will find flaws in my reasoning below.
According to logainm.ie, the name Monabrogue goes back to at least 1810. The Irish form given is Móin na mBróg, meaning 'Bog of the Shoes'. This is arguably a very odd name for a placename, which might indeed indicate that it is the corruption of an earlier form.
Again from logainm.ie, O'Donovan in 1838 speculated that it might have originally been Móin na mBurróg, with 'Burróg' presumably being a variant spelling of 'Barróg'. 'Barróg' can mean 'grip' or 'hold'. However, per Dineen's dictionary , there is a second - apparently unrelated - meaning of 'rod' or 'twig'. (This latter meaning isn't given in the more-modern Ó Dónaill's dictionary.) So using Dineen, the placename might have originally been 'Bog of the Twigs'.
(As an aside, per logainm.ie, there is only one placename containing the specific spelling 'na mBarróg', being Baile na mBarróg in Co. Mayo, which is anglicised as Ballynamarroge. O'Donovan in 1838 gives its meaning as 'town of the alders or nods'. This seems like an odd translation since (i) no dictionary I have gives such a translation for 'barróg'; (ii) the normal Irish for alder is 'fearn' or 'fearnóg'; (iii) I'm not sure what he means by 'nod'.)
From a search of loganim.ie, It turns out that there are five other placenames containing the element 'na mBróg'. And indeed, for one of those placenames (in Laois), there is a note included that speculates that 'na mBróg' (of the shoes) might originally have been 'na mBarróg'.
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Turning to 'Monamonnog', there is no mention of this form in logainm.ie.
The first possible meaning to occur to me for Monamonnog was Móin na Manach (Bog of the Monks). So it would be interesting to see if there was a monastery in the vicinity. However, mIlitating against this possibility is that Irish language names ending in 'ch' tend to be anglicised using 'gh'. (I think this has to do with the fact that English itself had a soft 'c' sound up to the end of the Middle English period, but it was kind of counterintuitively spelt 'gh' rather than 'ch'.) But if not 'gh', you might more likely expect 'c' or 'ck' to have been used in the anglicised form, rather than 'g'. In fact, doing a search of logainm.ie for the element 'na Manach' yields multliple results, with the anglicised form overwhelmingly ending in 'agh' (approx. 44 cases), with the runner-up being 'a' (only 3 cases). There were no instances of the anglicised form ending in 'og'.
Instead of 'Manach', possibly a more likely contender is some disyllablic word ending in the diminutive and derrivate suffix 'óg'/'eog'. However, for words ending in 'óg'/'eog', the anglicised spelling typically has 'oge', rather than 'og'. Assuming nonetheless that the word we are looking for does end in 'óg'/'eog', then it's going to be a noun in the genitive case plural, such that the whole placename takes the form Móin na Mxnóg (Bog of the Mxnógs) or Móin na Mxneog (Bog of the Mxneogs), where x represents a vowel, spelt either as a single letter, a digraph or a trigraph. Or, it could also have the form Móin na mBxnóg (Bog of the Bxnógs) or Móin na mBxneog (Bog of the Bxneogs), with 'm' eclipsing the 'B'. Plus, you could have double 'n' instead of single 'n' e.g. Móin na Mxnnóg, etc.
Below are all the words I could find on teanglann.ie that fit the above criteria. Unfortunately, it doesn't look like you can use wildcards in that website's word search, so my list below might not be exhaustive. In my opinion, the words in bold are the more likely candidates in the context of a bog.
mónóg (variant múnóg): bogberry, cranberrry
mionóg: fragment
míneog: gentle woman
muineog: (muine + eog) little thicket. Not actually listed in any dictionary but presumably such a word could legitimately be coined.
bánóg: small pasture, green patch
bonnóg (variant bannóg): bannock, scone
beannóg: leap, bound
beannóg: hood, corner of a cloak/shawl
binneog (variant beannóg): a cloth tied around the head [likely cognate with the previous]
buinneog: small shoot/sprout
banógh: virgin (literary word). Note sure if the 'gh' here would have been silent or pronounced 'g' in Ossory Irish.
It occured to me to search logainm.ie for these words in genitive plural contexts, in order to gauge the prevalance of each word in the placename database. The prevalance might then indicate the likelihood of a word being the one we're looking for. From a search, only two of the above words featured in placenames in the genitive case plural: 'na mBánóg' (five instances) and 'na Mónóg' (two instances). Note, all but one of the seven were anglicised using 'oge', the exception having 'oga'.
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Finally to the interesting part. I believe that a strong case can be made for a link between Monamonnog and Monabrogue on phonological grounds.
As far as I understand, the Irish of Ossory/Kilkenny could essentially be described as being Munster Irish, and so presumably the stress patterns would be the same as in Munster. In that case, for disyllabic words ending in óg/eog, as well as for the word 'manach', the stress would be on the second syllable.
With the first syllable starting with an 'm' sound, the second syllable starting with an 'n' sound, and with the stress being on the second syllable, then if the first syllable has a short vowel, there will be a tendency in rapid speech to omit the vowel of the first syllable, thus reducing the word to a single syllable starting with 'mn'. This type of reduction is not uncommon in Munster Irish when there is compatibilty of the relevant consonants. For example, in Munster, 'salach' is pronounced 'slach' (even when speaking slowly and deliberately).
Thus for instance, you could imagine 'manach' being pronounced as 'mnach', and 'mbinneog' as 'mneog'.
In cases where the 'm' is broad and the 'n' slender (e.g. 'mbuinneog'), or vice versa (e.g. 'mbeannóg'), my guess is that this reduction can still happen, but in such cases, one of these two consonants would have to change from broad to slender or slender to broad (since generally the letters in a consonant cluster must be all broad or all slender). But which of the two consonants would change, I don't know. (This is getting into irish language phonotactics, which I know hardly anything about.)
If, on the other hand, the first syllable has a long vowel, my guess is that this reduction to one syllable is far less likely to happen.
But, assuming that the word is indeed reduced to a single syllable that starts with an 'mn' sound (either broad or slender), this now enables another phonological phenomonen to come into play, as follows. In some dialects of Irish 'mn' (both broad and slender) is pronounced 'mr' e.g. mná becomes mrá, Luimneach becomes Luimreach. (Likewise, 'cn' becomes 'cr', 'gn' becomes 'gr', and 'tn' becomes 'tr'.) As far as I understand, this phenomonen was/is fairly widespread in Connacht and Ulster, and so possibly also affected Ossory Irish, although I don't think it affected Munster. Thus for instance, 'manach', could become 'mnach', which in turn could become 'mrach'.
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So now, you could imagine the following types of progression:
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Móin na mBonnóg -> Móin na Mnóg -> Móin na Mróg -> Móin na mBróg ('Mróg' is re-interpreted as 'mBróg' since the two words are pronounced identically. So I think that 'Bonnóg' is the perfect candidate phonologically, but not very likely semantically.)
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Móin na mBinneog -> Móin na Mneog -> Móin na Mreog -> Móin na mBróg(I'm assuming here - possibly incorrectly - that, in Ossory, slender double n was pronounced nʲ [like in English sin], rather than ɲ [like in English sing]. Also problematic is that, in the final step, there is a transition from slender 'mr' to broad 'mr'.)
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Móin na Mionóg -> Móin na Mneog or
Móin na Mnóg (not sure which of these two would occur)
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Móin na Muineog -> Móin na Mnóg or
Móin na Mneog (Not sure which of these two would occur)
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Móin na Manach -> Móin na Mnach -> Móin na Mrach -> Móin na mBróg (Possibly less likely since, in the final step, the transition is from 'ach' to 'óg')
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In conclusion, the following are my best guesses as to the original form, having factored in the semantic context (of a bog), phonological considerations, and the frequency of the second noun (in genitive plural contexts) in other placenames. A problem with the middle two is that they have a long vowel in the first syllable. And a possible problem with the last one is that it is not a dictionary word.
Móin na Manach (Bog of the Monks)
Móin na mBánóg (Bog of the Little Pastures)
Móin na Mónóg (Bog of the Bogberries)
Móin na Muineog (Bog the Little Thickets)
Btw, if the approx. timeframe of the transition from the older English form Monamonnog to the newer English form Monabrogue can be determined, this might provide a valuable datapoint in mapping the diffusion around the country of the mn -> mr shift (and associated consonant shifts).