Thank you very much, Jane and Elwyn, for your very helpful replies. I would like to add a little more information in case it would help to clarify the question about the name Owen.
I have done a lot of research about this Tully family (of Cornacarta,Carrickmac + Kildarra), including the 1901 censuses. Based on this and other family information, I'm guessing that John and Patrick Jr were brothers. Bartley may have been a brother of Patrick Sr. (This family, by the way, came from Co Roscommon and probably arrived in Cornacarta in the 1840's.)
John married Catherine Hasty in 1847. Their known children were Owen, Catherine, Patrick, John, Margaret, Thomas, Peter, James and Luke.
Patrick Jr married Margaret Grogan in 1854. Their known children were Ellen, Owen, Catherine, Anne, Bridget, Michael, Patrick and Austin James.
There is a Michael Tully who we think was a younger brother of John and Patrick Jr. He was only 17 when he got married in 1855. His sons were named Patrick, James, Michael, Thomas, Bartley and Martin.
The name Owen has not shown up anywhere else with the Tully descendants in these townlands, up to and including the 1901/1911 censuses.
As distinquished as the name Bartley is, it hasn't much helped me to find the relatinships. I found a Patrick Tully in these townlands who had "Barthow" as his father on his marriage record of 1885. I suspect that Barthow was a son of the 1st Bartley. This Patrick Tully's sons were Bartley, Richard, Patrick and Michael. (Unfortunately, I haven't been able to sort out who Bartley and Barthow are, who they were married to, or the names of their children.)
I will continue searching for an Owen Tully ancestor although it seems that I need to also consider Eugene or Eoghan. Since John Tully named his 1st son Owen and his 4th son John, it seems less likely to me that Owen, in this family, was another way of saying John. With what you've told me though, I'm not sure now!
An added question I have is how old a person would need to be to have his name put on the Griffiths Valuation. Would he need to be 21 or could a younger man (such as 18 or 20 years old) be put on there. I'm assuming that would make the younger man also responsible for the taxes to the landlord. (Michael Tully, for example, was not listed on Griffiths. He would have been 20 years old and already married in 1858. They lived in one of the 3 townlands mentioned but maybe sharing a house with others.)
If you have any other insights about the relationships between these men or the names, I would be very happy to hear from you again!
Thank you again,
Cindy