Philip Nawn born in Ireland in 1820. Immigrated to the US from Fermanagh, Ireland, Count of Allegiance in 1842. He became a US citizen in 1874. Can not find the name Nawn anywhere in Ireland. Was it something else?
The name is not common in Ireland but it does exist. Griffiths Valuation records 5 Nawn households in Fermanagh in 1862. One was in the parish of Clogher (in the townland of Gortmore); the others were all in the parish of Gallon (near Newtownbutler), in the townlands of Derrymacrow, Killard & Ports. I would therefore probably focus your research on those parish records if you have no other leads.
You need to know which exact denomination your family were in order to search the correct records. There were some RC Nawns in Fermanagh but the majority appear to have been Church of Ireland, certainly judging by the 1901 census.
http://www.census.nationalarchives.ie/
http://www.askaboutireland.ie/griffith-valuation/index.xml
The parish records are not on-line as far as I am aware, but copies are held on microfilm in PRONI, Belfast. (The Public Record Office).
Galloon C of I has no Nawn baptisms 1798-1830. It does have one mother listed as Sarah Naugher.
Bob Graham (County Fermanagh XO)
I did find two references to one individual. One spelled Nann and the other Naan.
Bob Graham (County Fermanagh XO)
If you search 1901 census you will find 47 Naan and 27 Nann and they are clustered around Fermanagh/Cavan.
Bob Graham (County Fermanagh XO)