What's the correct pronunciation of "Pádraigín"?
I believe the first syllable is "Pah" or "Paw", and the last syllable is "geen".
The middle syllable I'm not certain about. Is it "dray" or is it "druh", or something else entirely.
I suspect the answer, like many things in Irish, is going to depend on dialect.

/ˈpɑː(d)ɾəɟiːn/
https://forvo.com/word/p%C3%A1draig%C3%ADn/#ga
https://forvo.com/word/eithne_p%C3%A1dr ... 3%A1in/#ga

"Pádraigín" -I think it's pronounced as written in Munster.
In Conamara the D is silent, or even left out completely, and the G becomes a C (K sound).

On the cover of the CD Suantraí (Shanachie 78036) recorded by Pádraigín Ní Uallacháin (who is from Ulster), you find this explanation of how to pronounce her name :- padrickeen nee oolakawn.

oolakawn? Aye that's how English speakers pronounce...

I think Ulster speakers would pronounce [ˈpwæːdɾekʲinʲ ɲi ˈuəlˠəhanʲ]

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Is fearr Gaeilg na Gaeltaċta ná Gaeilg ar biṫ eile
Agus is í Gaeilg Ġaoṫ Doḃair is binne

I think she geared it toward English speakers. I doubt it's how she herself pronounces it.

Redwolf

But English speakers are able to pronounce [h] since it exists in English so it's better to use it instead of [k] as a pronunciation of broad ch... and it's the way it's pronounced in northern Ulster.
Same thing with the á : saying it's pronounced "ah" isn't more complicated than saying it's pronounced "aw" -- it's not pronounced "aw" in Ulster.

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Is fearr Gaeilg na Gaeltaċta ná Gaeilg ar biṫ eile
Agus is í Gaeilg Ġaoṫ Doḃair is binne

I am not sure about yours, but in my English there is no different between "ah" and "aw". Perhaps this is the case with whoever wanted to transcribe the name as well. It need not be wantonness :P

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ЯГОН ТОҶИК НЕСТ ИНҶО???