What does the H stand for in 'Jesus H Christ'?

It has special meaning.

It is short for the Greek word for "the" as in "Jesus the Christ".

"Christ" is a title, not a surname. Jesus' surname would have been bar-Joseph meaning son of Joseph.

See Matthew 16:20,

"Then charged he his disciples that they should tell no man that he was Jesus the Christ."

In Greek "the Christ" is "ὁ Χριστός". Now although we only see the letter "ὁ", in Greek the word would have been pronounced "ho"; the "h" was pronounced but not written. But when transliterated into Latin the "h" IS written.

According to the old biologist's joke, "Haploid". If you don't understand it, look it up or ask a biologist.

Harold... or maybe Holy? 

Harold.