Actually आप are wrong. I though the same thing for a while. Clannad is the name of an Irish band, The word, "Clannad," is short for Clann As Dobhar" which means "Children from Dore."
It's extremely confusing and a little disappointing, but the greatest ऐनीमे ever got its name because Jun Maeda misinterpreted the term, Clannad, and thought it ment family या clan. Still it has a nice ring to it. If आप don't believe me, go to the Clannad (Visual Novel) wikipedia entry. Then, read the settings and themes section. My proof should be in the सेकंड paragraph of that section.
