I was given my Mother's family name as a first name, and my Father's Mother's family name as a middle name. I think in Irish families, at least of two generations ago, there was a pattern/formula employed in the giving of Christian names;

First son, named after father's father
First daughter, named after father's mother
Second son, named after father
Second daughter, (perhaps named after mother)?
Third son, named after father's brothers

And I don't know how it continued (I'm basing this on observation of several families, you see.