Hi dtcoulson,
Not sure what information you've come across on adoptions during that period yet, if any and to be honest, I can't give you specific places to look. I can only share what I know of that period (family stories) and what I've gotten from going through records for my own family.
Adoption was definitely not a formal process in Ireland at that time and quite likely, if a family could not feed/keep their child or the parents had both died, it would be taken in by relatives; taken in by the church or sent to a farm, where it could be raised by staff to eventually work for them. Then there were some families that had the opportunity to get their children out of the country, albeit on the coffin ships to the US or Australia. If the child had no surviving relatives to make that decision, it would have gone to the workhouse and perhaps sent to the US or Australia.
I have about half a dozen surnames of families that seem to have lived close together in these regions and probably intermarried (and therefore mixed DNA) before there were records kept for us to read.
The diversity of romantic connections would have been limited. Remember this is back in an era where travel was a privilege and the population of your whole town was the equivalent to a present day housing estate. It's very likely that cousins married and there were brother-sister matches (siblings from one family marrying siblings from another)- it certainly happened in my family!
Furthermore, the mortality rate was higher and so were the marriage rates, meaning that often if a woman died young (say in childbirth of her 1st or 2nd), her husband would often marry her unwed sister, so she could take care of the child(ren). She would then go on to have children with him.
Surnames were also concentrated to counties in Ireland, bar a few very common names (e.g. there's Ryan's and Lynch's everywhere!), however, even with them there will be a root county (e.g. Ryan's, it's Limerick).
Your conundrum with the names is not necessarily to do with adoption. Look also at variation spellings, depending on what county's you are looking at. In my own family, I have a great x 3 grandfather, who's surname is Friary, yet his brother is Prior. Why? Because he's in Longford and his brother is in Cavan and there was mistake in the name when he registered at the Scrabby parish.
There are spelling mistakes aplenty in the Irish records, which morphed the names (e.g. Prior/Pryor/Friary/Friery/Freary/Frireagh) and there will be English and Irish versions used in some places on the border counties (e.g. Smith/Smyth/MaGouran/McGovern).
Look in to the history surrounding the surnames and you might find some of your answers.
Hope this info helps.
Michelle