The entrance to The Bombay Diocesan Council (C.N.I) in Mumbai.
Mumbai's switch was one of a number of city name changes in recent years, notably Chennai, which used to be Madras, and Calcutta, now known as Kolkata.
After the central government officially approved Mumbai's renaming, the city's civic body, the Bombay Municipal Corporation became the Brihanmumbai Municipal Corporation in early 1996.
But some other state institutions remained unchanged and Shiv Sena, now a junior partner in the state government, has unfinished business as far as the renaming programme goes.
Mumbai High Court?"All of the government institutions have to be changed," said Arvind Sawant, who wants the Bharatiya Janata Party-led central government to start by agreeing to Shiv Sena's demand to rename the Bombay High Court.
Shiv Sena lost power in 1999 and the renaming of the historic courthouse, which was established in 1862 under British rule, dropped off the agenda.
"The Bombay High Court should be the Mumbai High Court. I've raised the issue in Parliament and the government has to follow through with it. We are demanding that they change it now," the parliamentarian told AFP.
Law Minister Sadananda Gowda has reportedly agreed to put up the proposal before the cabinet before tabling it in Parliament.
Mr Sawant also has IIT Bombay in his sights but admits that persuading private establishments, such as the Royal Bombay Yacht Club and Bombay Gymkhana, to dispense with part of their heritage will be more difficult.
"We cannot force them to change their name but we expect them to and they should do it now," he said.
The director of IIT Bombay and the CEO of the Bombay Gymkhana both declined to comment when contacted by AFP.
"If they want they can change, but nobody can compel them to," Congress parliamentarian Husain Dalwai said, adding that Shiv Sena liked to trumpet "these emotional types of issues".
The Bombay Gymkhana Club in Mumbai
"Bombay" and "Mumbai" are used interchangeably. "Many people change what they call the city depending on what language they are talking in," said Naresh Fernandes, author of "City Adrift: A Short Biography of Bombay".
The names "reflect the multi-lingual character of the city", he added.
While the two names tend to live happily side by side, earlier this year musician Mihir Joshi fell foul of the Censor Board when it objected to his use of Bombay and bleeped the offending lyric out of his video.
"Mumbaikars" point out that Mumbai was the city's original name while some "Bombayites" feel the name change was too closely associated with the Bombay riots of December 1992 and January 1993.
"It's Bombay for me and always will be," Fernandes told AFP.
"I think because it followed so closely after the riots that to many of us, it was really a name change soaked in blood," added the writer, who covered the renaming of the city as a journalist.
But two decades on and with the city's youngsters having grown up knowing their home only as Mumbai, Bombay's time could soon be up.
"When my generation passes on, maybe Mumbai won't stick in the craw in the same way," Fernandes said.