I have never seen [name_u]Mirren[/name_u] spelled Muiranne before. It is a popular name here and is most popular with the [name_u]Mirren[/name_u] spelling but is also spelled Murrin or Murron. [name_f]My[/name_f] advice would be to go for the [name_u]Mirren[/name_u] spelling - I personally prefer spellings to be straight forward if possible.
I’d use the original spelling. [name_u]Mirren[/name_u], to me, is too tied to Dame [name_f]Helen[/name_f] to use as a name, whereas Muiranne strikes me as being of Irish origin. I’d pronounce them slightly differently, but that might be where the British and American accents differ rather than mispronouncing it - to me, Muiranne has a slightly softer Mh- sound at the start and an -an rather than -en ending.
I can’t see that Muiranne would get that badly mispronounced, but you’d have to weigh up how much it would bother you.
I’ve never seen this name before. If I were a teacher and this name was on my roll, this is what I’d guess:
Muiranne: (Moy rhymes with boy. Then [name_f]Ann[/name_f] with an R. Which is ran.) Moy-er-ann or Moy-ran
Muirin: (Moy rhymes with boy. Then rin, like the start of rinse.) Moy-rin.
[name_u]Mirren[/name_u]: (Meer, like a meerkat who is coming in.) MEER-in
Murron: (Mrr rhymes with Brrr, like you say when you’re cold and want the heater on.) Mrr-ON
I hope this impartial view into the mind of someone who doesn’t recognize the name helps you decide what you’d want to do.
I think it would be fine: it technically is not incorrect, just an Anglicisation. You also have that nice tie to [name_f]Helen[/name_f] [name_u]Mirren[/name_u], lending it a distinguished air.
I think there is a distinct difference between names with various established spellings, especially because of crossed culture lines, and spelling that have just been butchered. For example, [name_f]Isobel[/name_f], [name_f]Isabel[/name_f] and [name_f]Isabelle[/name_f] are all perfectly legitimate spellings, but [name_f]Madalynn[/name_f] is much more difficult to appreciate than [name_f]Madeleine[/name_f] (or even [name_f]Madelyn[/name_f], really).
In this case, I think [name_u]Mirren[/name_u] is just as respectable as Muiranne. It’s kind of like a [name_u]Vivian[/name_u] versus [name_f]Vivienne[/name_f] situation, both names are equally appreciable but elicit different images. It depends on preference.