Mar: मुंबई mumba’ī
Originally Mumbai was a group of seven islands [Bombay, Colaba, Lt Colaba, Mahim, Mazagaon, Parel, Worli] separated by malarial swamps; in the 14thC they were part of the lands owned by the Sultan of Gujarat.
The Portuguese arrived in 1534 and established a trading post and called it Bom Bahia [from Por: bom, ‘good’, ‘fine’; and bahia/baia, ‘bay’], which became Bombay under the British who acquired it in 1661 as part of Catherine of Branganza’s dowry when she married King Charles II.
The name Mumbai, although it sounds similar to Bombay, is derived from Mumba Devi, the city’s patron goddess and the kuladevata (‘clan deity’) of the Koli tribe, Mumbai’s original inhabitants. The original Mumbadevi temple was destroyed in the 17-18thC when the fort was being developed. Some say its ruins lie under Victoria Terminus railway station.
The modern Mumbai is India’s largest city (pop: 18.4m) and its economic powerhouse (GDP: $368bn). The name was officially changed in 1996.
For related place names see Indian Place names and Maharashtra place names.

Victoria Terminus, Mumbai fish-bone

Islands of Bombay 1893

Bombay, 1670 Nathan Hughes Hamilton