I checked through U.S. census records dating back
11 generations to 1742 and the individual’s name was simply O’Donoghue. That was the first time the name appears for my specific family line and as far as it reaches back. I believe that Donica is a name variant of O’Donoghue for this reason. I can provide you with the census report upon request.

Source #1:
Jeffrey Donica email 09.06.07
Source #2:
Jeffrey Donica email 22.02.15 see below
Source #3:
Source #4:
Source #5: