Citando a página da Wikipedia para a primeira sequela :
In the introduction, Sir H. Rider Haggard links the name Ayesha to Muhammad's wives, and the Arabic name (Arabic: عائشة, ʻĀʼishah, pronounced [ˈʕaːʔiʃa]), stating that it should be pronounced "Assha" /ˈɑːʃə/,[1] although the pronunciation A·ye·sha /ɑːˈjɛʃə/ or /ɑːˈjiːʃə/ is perhaps more common.
e aqui está a citação exata da nota do autor na introdução (ênfase minha):
In response to many enquiries he may add that the name Ayesha, which since the days of the prophet Mahomet, who had a wife so called, and perhaps before them, has been common in the East, should be pronounced Assha.