I'm a U.S. native speaker. (And, forgive me, I don't know the IPA).
I pronounce the name of the letter "H" as "aitch," with no actual initial "h" sound.
Until I read Peachey's post, I was completely unaware that anyone pronounces it "haitch."
The American Heritage Dictionary lists only the single pronunciation "āch."
So there must be differences in international customs. It's not the only one. To U.S. speakers the name of the letter "Z" is "zee;" to Canadians and British speakers it's "zed."
I have to wonder if the "haitch" pronunciation is a back-formation, in which people assumed that "aitch" must be an ignorant mispronunciation with a dropped initial "h" and added an "h" that hadn't originally been there.