Experienced genealogists are well aware of the naming patterns in Ireland and some other European countries. The first son after the paternal grandfather, the second son after the maternal grandfather, the third son after the father and the rest after uncles and the first daughter after the maternal grandmother, the second girl after the paternal grandmother, the third girl after the mother and so on.
These rules are not set in stone, however, but they are a tradition. There are stories about especially strong-willed parents refusing to follow the rules and naming their son or daughter after another person. That harms no-one but the poor genealogist trying to find their ancestor.
The parents may name the child after someone completely out of the picture. Baptismal names also cause confusion. At the baptism, the child is given an additional name, possibly after a saint. I have an aunt who changed her name back and forth on each census between her given name and her baptismal one. She finally used a completely different first name on her marriage license.
Watch out for this pattern when searching the census. Your mother may tell you that her father was named after his grandfather, say and you will search and search for the wrong first name. You are able to search a census with just a first name, especially in small towns.
Some ancestors did not change their given names to the more popular names in America or maybe the census taker would change the spelling as they had trouble communicating with the person answering the census questions.
If you see middle names in a compiled genealogy or family trees on the internet, be suspicious of those, as middle names were not used until about the 1790s.
Different spellings of surnames followed different countries. The Danes and some Norwegians spell Larsen, say with an “en,” whereas other Scandinavian countries use “on.” I saw Elef Larsen, Norwegian, his father was also Elef, for example, on the internet.
The Irish especially, use branch names as surnames. Sullivan, may be Liagh, Crath, Green, Comhane, Coomeen, Cumba, Comba, Ractury, Barruil, Shearhig, Keogh, Keagh, Burruil, Keach, Hurrig, Liah, or many others. Branch names were intered in the baptismal records.
The Harringtons and the Murphys also used branch names.
Coomeen, Coabach, and Trokirre may be Harringtons and Fuhur or Fuhir and many others may be Murphys.
There are other variations of surnames you must be aware of to find your ancestors. Sullivans at one time were called Lowney, for example.