The reason why you think it’s spelled that way is her name is often mispronounced. After she emigrated from Russia she changed her birth name, Alissa Rosenbaum, to a new name from a favorite author (who was perhaps Aino Kallas) and her typewriter (Sperry-Rand).
Ayn is an Anglicized version of a Finnish (Suomi) name and it is pronounced like Ein (eye + n), not Ann.