He chose “Bombay” in the second line of the song, he said, because he needed a rhyme with “today.” But by doing so, Mr. Joshi stumbled into one of India’s many unresolved tugs of war over history and identity.

Mumbai, a word drawn from the Marathi language, has been the official legal name of Mr. Joshi’s home city since 1995, when the nativist political party in power chose it to replace the Anglicized name Bombay, used since colonial times.

Not everyone adopted the new name, though. Some kept using Bombay out of long habit or institutional inertia — the city’s stock exchange and its high court still bear the name, for example. Others stuck with Bombay as a political statement, rejecting what they considered xenophobic politics behind the change.

Though this divide leads to regular dust-ups on televised talk shows, Mr. Joshi’s case was the first in recent memory in which an artist has been called out for using Bombay.

“If the name of this city has been changed, it’s only fair that we adhere to the new name,” said Meenal Baghel, editor of The Mumbai Mirror, a daily newspaper. “But should it have been bleeped as if it is a four-letter word? I think that’s ridiculous.”