Kimberly,
I am so glad you are enjoying you vacation here. Always good to hear. Part of IRO’s ethos is to encourage folk to visit our country. It is so pleasing to hear that you did come and that you have enjoyed your visit. You must come again!
You ask about the naming traditions. Ireland and Scotland shared the same tradition of naming children according to the following rules:
The 1st son was usually named after the father's father
The 2nd son was usually named after the mother's father
The 3rd son was usually named after the father
The 4th son was usually named after the father's eldest brother
The 5th son was usually named after the mother's eldest brother
The 1st daughter was usually named after the mother's mother
The 2nd daughter was usually named after the father's mother
The 3rd daughter was usually named after the mother
The 4th daughter was usually named after the mother's eldest sister
The 5th daughter was usually named after the father's eldest sister
The problem with relying too heavily on naming patterns is that, apart from the fact that not all families followed it, there are lots of things that can upset it. Common ones that I have encountered are:
When the father and either of the grandfathers have the same name. So you obviously can’t really have two or even three sons all with the same name, so a different name is needed though some families did actually use the same name again on the birth certificate, but differentiated with another more informal name for day to day use. So if you had two Georges (as per birth certs) you just called one of them something else eg Simon;
If a child dies young, then it was common practice to re-use the name for the next birth. But if you don’t know about the death, your analysis of who they were named after could be completely wrong;
Or if a close relative had just died and their name was used out of respect.
I have also noticed that many families liked to name the odd child after the local Minister/Priest, schoolteacher or a relative with no children of their own.
Sometimes people were christened with one name, but went by a different one (and would appear in censuses and other records by that alternative name), eg Henry & Harry or Ann & Nancy.
So for all these reasons, whilst tradition says, for example, that the 4th son was named after the father's eldest brother, it isn’t always so.
You ask how strong the naming tradition was in Donegal in the 1800s. Not a question I can really answer with any authority. One for the academics I suspect. Some families did and some didn’t. That’s what I have observed. I wouldn’t want to go any further than that.
You ask how common names were. For Arthur, the short answer is not very common at all. In the 1901 census for the county, out of 86,057 males, only 162 were named Arthur. But most of the other names were very common.
I assume you know your McClintock ancestors are almost certainly of Scottish origins, arriving "across the sheugh" in the 1600s? MacLysaght’s “The Surnames of Ireland” says of MacClintock: “ Mac Giolla Fhionntog. A Scottish name numerous in Antrim and Derry. Black says this, like MacClinton, refers to St Fintan.” (Black is the acknowledged expert on Scottish surnames). The Muster Rolls for Ulster (Men & Arms) c 1630 edited by RJ Hunter lists at least 5 families in Donegal then. Alexander McLentock, Fynlay McClentock, John McClentock, John McClintog & Patrick McClintog. So around 5 families were established in the county in the Raphoe area (around Lifford) in 1630. Others will likely have followed.