Connolly family tree has her name as Isabell Elizabeth. Ireland births and baptisms index has it as Elizabeth. She also may be known by "Bell" and "Isabella" and last name aka "Daily."
On April 2, 1911 she was recorded in the Ireland census, living in Reclain, Clonavaddy, County Tyrone with daughter Bridget Anne, James Hagan (age 8), and Edward Quinn.
I am uncertain as to is Elizabeth and Isabella (Essbella) are the same person or two different people. The 1851 census record for her has a note that says something like "No (?) of Elizabeth sheet 22 (the unclear word following the word "No" begins with an "r"). I've located an 1870 death record for Elizabeth Daly, but only a transcript not the original record. If this is her, no idea why she's listed undfer her maiden name.
One possibility is that Patrick Hamill married Elizabeth Daly in 1867 and that they had three children. The birth records for all three list their mother's name as "Elizabeth." The second child, James, was born 5/4/1870. This third, Charles, was baptised 9/28/1871. The death record for Elizabeth Daly is 7/2/1870. There is to be insufficient time for ELizabeth to have had Charles in between the birth of James and her own death. It is possible that Charles was born in 1869 and for some reason not baptised until 1871. Records also indicate that Charles died in 1871.
The question arrises because the birth records for the additional children of Patrick show their mother with the name "Isabella" or "Bella", as do the 1901 and 1911 Ireland Census records. "Isabella" is a form of the name "Elizabeth." Did she start referring to herself by this name after 1870? Or did Elizabeth die ca. 1871 and Patrick then married her sister Isabella? The 1851 census for Elizabeth Daly shows her parents and siblings, including two deceased sisters. Plus a sister names "Essbella." But it bears a handwritten note about Elizabeth that is impossible to completely read. Does this document indicate that there were sisters ELizabeth and Isabella? Or is the note an indication that Elizabeth is not a member of this family?