The name "Bombay" is derived from the Portuguese words "Bom Bahia", which means "good bay". This name was given by Portuguese explorers in the 16th century. The name "Mumbai" is derived from the name of a local goddess, Mumbadevi.
The change of name from Bombay to Mumbai was motivated by several factors, including the desire to use an Indian name for the city, to reflect its history and culture, and to differentiate it from other cities with similar names.