The Greek pronunciation is "ahs-pah-SEE-ah". (That is how my father's friend, a woman from Greece named Aspasia, pronounces her name.)
Also, "Aspasia" is a genus of 7 species of orchids occurring from southern Mexico to southern Brazil. According to the "Encyclopædia of Cultivated Orchids" by Alex D. Hawkes, 1978 edition, the genus is pronounced "as-PAZ-ee-ə".
Aspasia Manos (1896-1972) was the commoner wife of Alexander I, King of the Hellenes (Greece). Due to the controversial nature of their marriage, she was only ever titled as "Princess of Greece and Denmark". She is the mother of Queen Alexandra of Yugoslavia, and the grandmother of the current pretender to the throne of Yugoslavia, Alexander, Crow Prince of Yugoslavia.