Only call her 'Niamh' if you are going to pronounce it correctly - 'nee-uv' (or, where I'm from 'nee-iv', but close enough!)
'Neve' is not necessarily a alternative spelling of Niamh. Neve Campbell's name is a surname, as are Neave and Nieve. I believe Neve is also a variant of the name 'Neva', which is of Latin origin and means snow.
I am from Northern Ireland, and I used to really prefer traditional spellings of Gaelic names; however, after reading the Baby Names threads for a while, I now don't give a stuff, as most of the people who get very judgmental about names seem not to know much about them.
I don't see why 'Neve' is considered unacceptable but 'Aidan' is fine (and, somehow, the 'correct' spelling), when 'Aidan' is also an Anglicisation (see also Maeve, Orla).
I don't understand why people should always spell 'Caitlin' that way, and then pronounce it in a way that 'Katelynn' would represent better, rather than the correct pronunciation; it seems that Niamh also falls into the group of names which it is better to spell 'correctly' and pronounce wrongly than to change the spelling to one which accurately reflects the pronunciation.
OP, use whatever spelling you prefer.