Darragh,
Dara, and
Dáire are all versions of the same name! I did a little bit of research and found that
Dáire was one of the most popular names used in
Ireland before 1100 according to M.A. O'Brien's Corpus Genealogiarum Hiberniae, so you can rest assured the name
Dáire has been around for a long time. Before that point I could only find possible related names, such as Daighre in 1056. I found Modarra as a surname around 1600, but I could not find many historical records of
Darragh or when that spelling first arose. I hope this helps!