The outlet, which sells Western men's wear, opened 10 days ago in Ahmedabad city in the western state of Gujarat with "Hitler" written in big letters over the front and with a Nazi swastika as the dot on the "i".
"I will change it [the name] if people want to compensate me for the money we have spent – the logo, the hoarding, the business cards, the brand," Rajesh Shah told AFP.
He put the total costs at about $2 700.
Shah insisted that until the store opened he did not know who Adolf Hitler was and that Hitler was a nickname given to the grandfather of his store partner because "he was very strict".
"I didn't know how much the name would disturb people," he told AFP by telephone from Ahmedabad. "It was only when the store opened I learnt Hitler had killed six million people."
Members of the tiny Jewish community in Ahmedabad condemned the store's name, while a senior Israeli diplomat said the embassy would raise the matter "in the strongest possible way."
"People use such names mostly out of ignorance," Israel's Mumbai Consul General Orna Sagiv told AFP.
Esther David, a prominent Indian writer in Ahmedabad who is Jewish, said she was "disturbed and distressed" by the shop, but added that some Indians used the word "Hitler" casually to describe autocratic people.
David said Jewish residents had sought to change Shah's mind about the store's name and told him about the Holocaust.
The row evoked memories of a controversy six years ago when a Mumbai restaurant owner called his cafe "Hitler's Cross" and put a swastika on the hoarding, claiming Hitler was a "catchy" name.
The restaurant owner eventually agreed to change the name after protests by the Israeli embassy, Germany and the US Anti-Defamation League.
Hitler attracts an unusual degree of respect in some parts of India, with his book Mein Kampf a popular title in bookshops and on street stalls
Gujarat schoolbooks issued by the Hindu nationalist state government were criticised a few years ago for praising Hitler as someone who gave "dignity and prestige" to the German government. – Sapa-AFP