It has come to "Bombay"

Cow is also mother. Therefore she's addressed as amba. Amba means mother. Still in Gujarat province, they call amba. And in U.P., United States, er, United Province, in India, they also call amba, or in a broken language they call amma. Still... That is from very long time, mother is... Amba-devī. There is a... From Amba-devī, there is a big temple of Mother Durgā, Kālī, in Bombay. So this Amba-devī was pronounced by the Englishmens as Bamba-devī, and from Bamba-devī it has come to "Bombay." Actually, there is a big temple of Amba in Bombay. From that name, instead of Amba, they have become Bamba.

Śrīmad-Bhāgavatam 1.16.19 -- Hawaii, January 15, 1974