Wow, this topic was really buried under all those other threads!
Myra is interesting, but I think I still prefer the sound and look of
Muirne. I also like
Muriel, but I prefer the similar
Mariel.
I don't see many un-Anglicized Irish names around here, but maybe that's because I'm on the west coast. Most of the time they are Siobhans (unfortunately considered ghetto) or little Saoirses (probably influenced by the actress).