in confluence with the avoiding situation exposed by Anneza.
I checked in babynamesofireland.com (because there are audio records of the names) and in Irish Muirgheal is pronounced with a sound [u] (in a way very similar to Muriel in Catalan or in Spanish), so the adaptation of Muirgheal as Muriel through the Latin or even through the French/the Norman has a lot of sense. And I can see the evolution from [u] to a schwa and then to [e] or [a].
Since Muriel is an old fashioned name in English, I didn't hear it in real life (I think) and I don't know if nowadays in the English of IrelandMuriel is pronounced with [u] (like in Irish) or with [ju] (like in the general modern English pronunciation). Next Monday I will ask my English teacher about the pronunciation of Muriel in Ireland.