My name is pretty unpronouncable. I realise this every time someone goes to introduce me. I was doing workshops in schools the last two weeks; then a talk to an MA class; then a podcast interview with an American site - each time the person who introduced me either asked how to pronounce my name, or gave it their own special pronunciation. Irish, Americans, Antipodeans and Europeans alike have difficulty with my name. It doesn't help that my surname (which is the Irish for O'Connor, btw) sounds nothing like the way it looks.
So, here is the from-the-horse's-mouth guide to pronouncing Nuala Ní Chonchúir:
Nuala - pronounced NOO-LA (rhymes with 'hula', as in 'hula hoop')
Ní - it sounds the same as KNEE (as in 'knee cap him')
Chonchúir - it has two parts: the first part sounds like CRUH (as in the start of the word 'crutches'); the second part sounds like HOOR (as in 'she's a mad hoor').
NOOLA KNEE CRUH-HOOR
NUALA NÍ CHONCHÚIR
See? Simple, when you know how!