Haitch/aitch story.
A couple of years ago I was watching the U.S. national spelling bee (don’t y’all dare call me a geek) and the animator asked one little girl to spell aitch. “Aitch” she said with confusion. “Aitch” he said with authority.
“Um, can I get a definition please?” again with some confusion. I believe he said something like “aitch is the eight letter of the alphabet.” So, she, being from non-continental U.S. said “Haitch??” “aitch” he says. Poor thing got it wrong.
That doesn't seem like it would be a legal word for a spelling bee. You can't definitively spell letters, they are what they are. That's like trying to spell "a". Is it ai, aye, ae, aeh?
About "a/an h-", In the three Jane Austen books that I just finished reading, I noticed that all words starting with "h" had the article "an", no matter how they were pronounced.
