City of Bombay
The name “Bombay” is actually an English distortion of the original Indian name, which is the name of the “godess” of the city (the name means “great mother”). The temple of this idol is located in the middle of the city, and it is worshipped by the majority of the population of the city until this day. Should there be a problem of “בשם אלהים אחרי לא תזכירו” to pronounce the Indian name of the city?
The prohibition to mention and use the name of Avodah Zarah, is to refer to the name of the Avodah Zarah itself. A city which is named after Avodah Zarah, but no longer refers to the Avodah Zara but rather to the city, would not be included in this prohibition. Bombay is one of the biggest cities in the world, home to close to 40 million people. Certainly not more than a tiny fraction make their way regularly to this temple. In addition, being an international city, to most of the world Bombay refers only to a city, not a foreign god.
In addition, Bombay is in fact more than a distortion of the original name, but rather a totally different name. The other name for the city Mumbai, is a derivation of the Avoda Zarah, named Mumbadevi. Bombay, was the name given by the British in the 17th century when they controlled the city, and comes from Portugese, meaning “good little bay”. This name certainly has no question of Avodah Zara. Based on the above it would seem there is no problem with the name Mumbai as well, which is also not the actual name of Avoda Zara, and to most of the world is not even a reference to such.