You say that your Graham family came from Tattygare. I assume this is them in the 1901 census (note that Tattygare is in Co. Monaghan rather than Armagh):
John was born in Armagh whereas Sarah was born in Monaghan.
Same family in the 1911 census:
Here’s their son Hugh’s birth in 1881:
Hugh senior died 15.5.1885 aged 87:
Here’s Hugh’s daughter (Grimes) who married John Gormley in 1880. So did a Grimes marry into the Gormley/Graham family? Is that the Grimes connection:
With regard to the spelling of names, we have quite a few interchangeable surnames in Ireland. Other examples I have come acorss are Nogher/Connor, Kirkpatrick/Kilpatrick, Faulkner/Falconer, Robertson/Robinson & Uprichard/Bridget. Grimes/Graham looks to be another. I don’t think it’s anything to do with the British administration, more a local custom. (In some cases you can trace it back to the way an Irish name was anglicised. When translating a name from Irish there can be several different English words, and so that can lead to multiple names). Ireland has always had a fairly relaxed attitude to spelling and to multiple names. Many people weren’t literate but even when they were, they didn’t really care much how their name was spelled either. According to MacLysaght’s “Surnames of Ireland”, Graham is a “Scottish name very numerous in Ulster, is used as an anglicised form of two Irish surnames namely Gormely & Grehan.”
Tattygare is in the RC parish of Clontibret. Their records only start in 1860 so you will probably struggle to get back further than that if the family originate there. But if they originate in Armagh you would need to search adjacent parishes to the north.
I don’t see any Graham/Grimes/Gormley farm in Tattygare in the tithe applotment records for 1830, so possibly the family arrived in the townland after that. There's a Hugh Grimes is listed farming 8 acres in the townland in Griffiths Valuation for 1861. That puts the Grimes family in the townland then but I think the Graham/Gormley family came from elsewhere. John's townland is Doogray on the marriage certificate but I am not sure where that is.