I always thought it came from the Lord's Prayer, Harold be thy name. Have have heard this several times from different people today , hoping it's really blasphemous and I will try and say it more.
You probably know this but it's "hallowed be thy name", hallowed meaning, revered. Although that is one of the explanations, that it's an ironic permutation of "hallowed".
Here are a couple of other explanations out there in the Googleverse:
"Apparently a wit noticed the middle letter in the familiar monogram IHS (Iesus Hominum Salvator - Jesus, Savior of Men) and decided that it was fodder for humorous speculation."
"H stood for Haploid since Jesus has no human father."
"H derives from the taunting Latin inscription INRH that was supposedly tacked on the cross by Roman soldiers: Iesus Nazarenus, Rex Hebrei (Jesus the Nazarene, King of the Hebrews). Trouble is, the inscription is usually given as INRI: Iesus Nazarenus, Rex Iudaeorum (J.C., King of the Jews)"