I am too.
The link you showed Aghadowey was for a Thomas McAuley Woods born to Thomas Woods and Maria Woods formerly Bolton. On the link the birth is 26 September 1900. The date of 15 August is mentioned in a post. Where has this date come from? I always understood that a birth certificate showed what the family had decided to call the child. Although there are many stories about this including fathers forgetting or not knowing the correct spelling and birth being registered late and so have a birthdate that fitted in with the time frame for registration but not with the date of the actual birth.
Whether or not these names were continued over time was a matter of luck, chance, consistency etc compounded in those days by immigration, poorer access to education and accents on immigration.
My Grandmother was sure that her middle name was Buchan or some times Buchanan. Later looking at her christening entry COI Ballykelly it seems to have been recorded there as Banigan, Bannigan while her cousin 5 years older had this B name recorded as Bamingham and older ones as Birmingham and Bermingham. So my grandmother has her NZ death certificate with Buchan on it. Her COI christening entry has Bannigan. But she is one and the same person.
Dinny unless there were several Woods born on that date in 1900 then it is quite possible and highly probable that Thomas McAuley Woods is Thomas Bolton Woods. Often this may have come about if say the mother had died early or the family had named the McAuley after a then family friend who over the passage of time was no longer such a close family friend. You may be able to find when your Thomas started using the Bolton by looking at his marriage certificate, children's birth records etc .