This one has an unusual 'flat' sound in it - not 'Maureen' (which is Mairín, different as you can see) or the equally easily confused Moreen but more similar to the sound of the word 'myrrh'. Muir means 'sea' - think of it as Mer in mermaid, then add a y sound in the back of the mouth after the M - M'yer. The second element is from fionn meaning 'white' and in Gaelic is pronounced not as a diphthong but a quick 'syllable-n-a-half'. So M'yer-e-ann should get you there.
The 'een' sound in Gaelic is indicated not by -eann but by -ín.