"The joke has worn thin. I'm tired of having your opinions ascribed to me. Pls tweet under your own name. Thanks", the author had tweeted to the account.
The handle with more than 30,000 followers adopted a "faux Rushdie persona" and engaged in debates with right-wing accounts.
The owner immediately capitulated and changed his handle to @IndiaExplained.
"It gave me a chance to pay homage to Rushdie and other writers while being able to reflect and comment on things that matter to me", the owner of the account, Rohit Chopra told Indian news website Scroll.in.
But many Indians online have taken exception to Sir Salman's stance, accusing him of both lacking a sense of humour and clamping down on freedom of expression.
With its new name, the account has promised to provide "satirical and political commentary on India".
It is just one among a number of Indian parody Twitter accounts which have courted controversy with those tried to send up.
In one instance, the office of former Indian Prime Minister Manmohan Singh asked Twitter to block the account of @PM0India (which used a zero instead of a 'O') because of "objectionable content", which "could be mistaken as the official account of the PMO and have serious ramifications."

County Durham and Darlington Fire and Rescue crews were called to Beech Close, Brasside, on Monday evening. The street is in the Framwellgate Moor area of the city.
The man was pronounced dead at the scene.
A joint investigation between the fire service and Durham Police has been launched, a fire service spokesman said.

25 November 2016 Last updated at 07:57 GMT
It was given to the London museum in 1905 by a rich business man and the giant skeleton has been amazing visitors for many years as they enter the museum's main hall.
It isn't a real dinosaur but a life size plaster replica of the skeleton of a Diplodocus.
Now Dippy is on the move on a trip around the UK, watch this video to find out more.

Matthew Gordon said he never "cut corners" when it came to maintenance and spent more than Â£6,000 in a year on repairs to the truck.
He told Bristol Crown Court if the lorry had been unsafe he "would have done something about it".
Mr Gordon, 30, of Dauntsey, Wiltshire, denies 14 charges against him.
Mr Gordon, the owner of Grittenham Haulage, is defending himself following the crash on Lansdown Lane on 9 February last year.
Mitzi Steady, four, Robert Parker, 59, Philip Allen, 52, and Stephen Vaughan, 34, died in the crash in 2015.
The lorry hit several pedestrians, including Mitzi, from Bath, and a car containing Mr Allen and Mr Vaughan, both from Swansea, and Mr Parker, from Cwmbran, south Wales.
Driver Phillip Potter, 20, also of Dauntsey, denies causing the deaths by dangerous and careless driving. He is also charged with causing serious injuries to Karla Brennan and Margaret Rogers - Mitzi's grandmother - by dangerous driving.
He denies a total of 10 charges against him.
Peter Wood, 55, from Brinkworth, Wiltshire, a mechanic who carried out safety checks on the truck, denies four charges against him.
The trial continues.
Salman Rushdie has been pilloried by Indian tweeters after confronting a parody account @RushdieExplains.
[NEXT_CONCEPT]
A man has died in a house fire in County Durham.
[NEXT_CONCEPT]
Dippy the Diplodocus is one of the Natural History Museum's most recognisable residents.
[NEXT_CONCEPT]
The owner of a lorry that crashed on a steep hill in Bath killing four people has told a jury he did not think the vehicle was unsafe that day.