Brenda, you don’t give the name of your g g g grandmother. Since Geogheghan is such an unusual name in the Isle of Man, I’m guessing that you’re referring to Ursula Geogheghan.
I’m also guessing that you don’t have the census pages for 1891, 1901 and 1911.
In 1891, Ursula was listed as “niece”, age 10, born in Ireland, living in Douglas IOM with Francis Otterson and Elizabeth Otterson nee Geogheghan.
In 1901, Ursula was a 21 year old domestic servant b Co Meath Ireland, living with a Colbert family in Blackpool Lancashire.
In 1911, Ursula (age 30, born in Dublin) was with husband Peter McGuinness (married in 1906) and their 3 small children, lodging with Francis Otterson and Elizabeth nee Geogheghan (born Cull Mullin, Co Meath, Ireland) in Blackpool.
I’ll attach 2 adjacent scans of baptisms in Douglas, IOM, from familysearch.org:
1) Thomas Joseph Otterson, born 4 Sept 1891, baptised 27 Sept 1891, father Francis Otterson, mother Elizabeth Geogheghan.
2) Ursula Geogheghan, born 20 April 1881 (no indication of birthplace), baptised as a 10 year old on 1 October 1891, mother Elizabeth Geogheghan.
So, when Francis and Elizabeth Otterson took their baby, Thomas Joseph, to be baptised on 27 Sept 1891, were they persuaded by the priest to make arrangements a few days later for their 10 year old “niece” to be baptised ?
There seem to be 2 possible interpretations from a combination of all these records:
a) Elizabeth Geogheghan was the birth mother of Ursula (in Dublin or Co Meath ?). Perhaps she left Ursula in a convent (where ? perhaps where the birth had taken place) and collected her later when she was married to Francis Otterson (St Peter’s Priory, Liverpool, 27 April 1884). They referred to Ursula as their niece to avoid revealing her illegitimacy.
b) Ursula was the illegitimate child of a sister of Elizabeth Geogheghan. Elizabeth took her niece from the convent and welcomed the child into her family after her marriage to Francis Otterson in 1884. In 1891, she gave her own name as the mother of 10 year old Ursula at Ursula’s baptism.
I think suggestion a) is the more likely one.
Let me know if you’d like to see scans of the census pages.