So to me the unvoiced 'hhhh' sound means you say 'haitch' doesn't it? How do you say 'hhhh' and have it end up as 'aitch'?
By that logic, we would all be saying Lell for L.

We aren't talking about the various sounds the letters make, we are talking about the names of the letters.

The letter H is pronounced aitch. The letter L is pronounced elle. The letter M is pronounced em. And so on.