I have just written a column on the name
Cara (and
Kara). Its history of usage seems to me to show that it was originally mostly a pet form of
Caroline, with some help from the Latin. The word "cara" meant in Latin about what it means in modern Italian, but the first references to that meaning go back to Latin, not Italian, and it has never been used as a name in Italy, so I think it was learned people in Scandinavia who first used it based on the Latin meaning.
I think it was only after
Cara was established as a name that people noticed it accidentally was the same as the Irish word for "friend" and started using it thinking of that as the derivation.
Cara does not seem to have been used as a name in ancient or medieval
Ireland, and I so far have not found any references to the possible Irish derivation before the 20th century.