All I can say is that is how it was spelled in the records I looked at, there was also Neary but no more than a few.
Same with Griffith Valuation more were spelled Nary than
Neary. Spellings were pretty flexible in the 1800's, so many people couldn't spell their own names, that shows in the 1901 Irish Census. The writer may have just written down what they thought they heard or just went for the easy spelling. Certainly isn't that unusual in Ireland.
In the telephone book for Clare there are 11 Neary/0 Nary listed, might be worth investing 11 stamps, addresses sufficient for delivery. Also listed 17 Sligo/Mayo.
8 Shanahan Galway, 30 Clare.