She accuses him of talking the name in vain (a sin, this references one of the 10 Commandments), and his response that he doesn't even know the name she is referring to, places the protagonist in the same shoes as Peter, denying Christ right before his execution (another betrayal). I guess the question is what does 'the name' refer to here? I interpret it this way. I feel like, as mentioned in the other posts, the man in this song views the man/woman union as a holy one in its ideal form (this is the 'Hallelujah'), and the woman does not see it this way. I get the sense in this verse that she accuses him of taking the name in vain, with the name being their love/relationship. I imagine he does this when it falls apart, and he curses it, but he says "So what if I did, really, what's it to you?" with the implication that she doesn't believe in that anyway. This framework is introduced in the very first verse "I heard there was a secret chord that David played and it pleased the Lord...but you don't really care for music do you?". Right at the outset, she is rejecting his world-view regarding the religious component of relationships. The last line of this verse tells me that the carnal/spiritual duality of relationships both have a greater truth to the protagonist, either the 'holy' or the 'broken' Hallejulia. Both have the blaze of light (truth), but just a blaze, as each is incomplete without the other half.