I always thought it was a play on Clemenza's name, which translates loosely into clemency/mercy. I thought it was a play on the darkeness of Godfather II, where mercy is replaced by the wrath of god as in the second coming.

The fifth angel emptied his bowl over the throne of the beast and its whole empire was plunged into darkness. Men bit their tongues on account of the pain, but instead of repenting for what they had done, they blasphemed the God of heaven because of their pains and sores. See Rev. 16:10.