from Slater's commercial directory of 1870 - Nobility, Gentry & Clergy section
John Bermingham, Esq. J.P. Millbrook, Tuam
I'm not sure what the J.P. stands for..
there are a few Bermingham references around Co. Galway - Galway city, Loughrea, Dunmore & Gort
they seem to derive from '..the Berminghams, barons of Athenry'
The directory entry for Dunmore mentions 'Bermingham Castle, a beautiful ruin, once the seat of that ancient family'. Dunmore is described as 9 miles NE of Tuam
the only entry I see with the 'i' spelling of the surname in Co. Galway is a Grocer in Main st, Loughrea named Redmond Birmingham. he's also listed under the Ironmongers and Hardwaremen section.
Shane