Interesting information. Most likely the names Helen and Cornelius were given because the parents had those names, Helen and Ellen being interchangeable. My extended Carroll family had both other names you mention - Daniel and Edward/Edmond - the latter twonames being interchangeable.
Since Buttevant is part of the CLoyne diocese, have you ever had a search done at the Mallow Heritage Center to be sure you have the names of all the children baptized there? And do you also have the baptismal sponsors' names?
My Carrolls must have been the poor cousins. My ggrandmother was V. Ann. She went by Ann, but since the name Veronica was used in the next generation, I would guess the V. stood for Veronica. From the names of baptismal sponsors I know she had a sister Ellen and a sister Peggy/Margaret as well as a brother Denis. She also had siblings Edmond, Mary, Catherine, and Anthony. A Daniel Carroll lived in the same townland. I am talking the early 1800's up to 1837 for the birth of these siblings. I have no idea where they went after about 1850. I have spent over 20 years trying to trace them.