Jesus’ middle name was not Harold.
His last name wasn’t Christ either.
The phrase “Jesus H. Christ,” meaning the equivalent of “for crying out loud,” probably morphed from similar phrases like “holy Christ,” or “for Christ’s sake.”
If the H stands for anything at all, it just as well could stand for “Holy,” as in “Jesus Holy Christ,” to make the exclamation sound even more severe or shocking.
Most likely, though, it doesn’t stand for anything but just feels satisfying to say.