The good old historical names of Indian cities have been changed by Muslim invaders and later by the British for their convenience. We, Indians had to accept and are used to these names for the past 200 - 500 years.
The renaming of these cities was proposed in 1947, soon after India got Independence. After a lot of controversies, many of the proposed changes were not accepted by the Central Government. However, over the time many changes are accepted and names of the cities are changed back to their original names, Trivandrum - Thiruvananthapuram, Bombay - Mumbai, Madras - Chennai, Cochin - Kochi and so on. The most recent changes were of Orissa - Odisha, and Pondicherry - Puducherry.
Lately, a lot of buzz is going on to rename Allahabad as Prayag. The name Prayag has got a lot of history behind and was mentioned even in Vedas and Puranas as Lord Brahma is said to have performed the first Yagna there. Prayag was changed to Illahi-bad by Mughal king Akbar during his reign. Now the politicians and activists are demanding it to be renamed as Prayagraj.
Coming to the facts, even though Madras is renamed as Chennai, still the Madras High Court holds its old name. The same case with IIT Madras. The Mumbai Stock Exchange is still called as Bombay Stock Exchange. The names and brands are deep routed in Business and it may affect them adversely if the names are changed. Moreover, it sows confusion and involves huge costs. There are many things to be changed, Rail and Roadway signs, stationery and paperwork across the country have to be updated.
Although modern thinkers may opine that the entire process is a waste of money and investment, following the sentiments of millions of Indians, the names of cities have to be changed back to their original names to retain the culture and heritage of India.