Hey there! Got a Moira of my own.
There are two legitimate ways of pronouncing the name, Maw-Rah & Moy-Rah, we do that latter.
Some people do have a LOT of trouble getting it out, my mother in law for the first six months of Moira's life butchered it!
However, I've found that if a person has had some exposure to another language, they have little to no issues saying it the way we do.
On top of all this, when I do meet someone who has a friend or relative w/the name they are quick to smile and tell me about their namesake. For example, when Moira was about 6 months old we were on vacation down the shore. A little old Irish late admired her in the stroller and then asked her name. I introduced her as Moira. The lady smacked her hands on her own cheeks, and let out a wow! Apparently she had immigrated from Ireland years and years before and had never heard anyone in the States with the name. She proceeded to tell me a story about her friend named Moira, which she claimed meant Little Mary. She left with the biggest smile on her face.
I love it, and have even asked our Moira if she likes her name. Her response, "Yup, it's really cool mom." :)