When the city of Bombay was renamed into Mumbai in 1995, it was a different kind of name change than, say, Peking to Beijing. Rather than correcting pronunciation, the city chose a different etymology.
The official reason for the change was to undo colonial anglicization of the city's original name, so called after its patron deity Mumbadevi. Her name, in turn, derived from the Sanskrit Mahā-Ambā Devi, Great Mother Goddess.
The name Bombay, however, can be traced back to the Portuguese conquerors of the 16th century, who called the place Bom Bahia, or good bay. This name was indeed later anglicized to Bombay. But linguistically there is no relation, let alone corruption, between Bombay and Mumbai - and it seems a curious coincidence that the two names sound so alike.
Over a decade before the name change, Salman Rushdie told the tale of the city's origins in his novel 'Midnight's Children' (1981):
...at the dawn of time, when Bombay was a dumbbell-shaped island tapering, at the centre, to a narrow shining strand beyond which could be seen the finest and largest natural harbour in Asia, when Mazagaon and Worli, Matunga and Mahim, Salsette and Colaba were islands, too - in short, before reclamation, before tetrapods and sunken piles turned the Seven Isles into a long peninsula like an outstretched, grasping hand, reaching westward into the Arabian Sea; in this primeval world before clocktowers, the fishermen - who were called Kolis - sailed in Arab dhows, spreading red sails against the setting sun. They caught pomfret and crabs, and made fishlovers of us all. (...)
There were also coconut and rice. And, above it all, the benign presiding influence of the goddess Mumbadevi, whose name - Mumbadevi, Mumbabai, Mumbai - may well have become the city's. But then, the Portuguese named the place Bom Bahia for its harbour, and not for the goddess of the pomfret folk ... the Portuguese were the first invaders, using the harbour to shelter their merchant ships and their men-of-war; but then, one day in 1633, an East Indian Company Officer named Methwold saw a vision. This vision - a dream of a British Bombay, fortified, defending India's West against all comers - was a notion of such force that it set time in motion. History churned ahead; Methwold died; and in 1660, Charles II of England was betrothed to Catharine of the Portuguese House of Braganza - that same Catharine who would, all her life, play second fiddle to orange-selling Nell. But she has this consolation - that it was her marriage dowry which brought Methwold's vision a step closer to reality. After that, it wasn't long until September 21st, 1668, when the Company at last got its hands on the island ... and then off they went, with their Fort and land-reclamation, and before you could blink there was a city here, Bombay, of which the old tune sang:
Prima in Indis,
Gateway to India,
Star of the East
With her face to the West.