The word 'aitch' is pronounced without a starting 'h' sound, unlike 'hotel' or 'hat'. Listen closely to native speakers; they say 'aitch', not 'haitch'.
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Accent Variation
Some English accents may add an 'h' sound to 'aitch', but it's traditionally silent. In some Irish accents, people pronounce it as 'haitch'.
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Letter Naming
In English, 'aitch' refers specifically to the naming of the letter 'H', not the sound it produces. She spelled 'hotel' as 'hotel' but pronounced the 'H' as 'aitch'.