The shop, which sells Western menswear, opened in Ahmedabad city in the western state of Gujarat last month with "Hitler" spelled out in large white letters above the storefront, complete with a Swastika as the dot on the "i".
Members of the tiny Jewish community in Ahmedabad condemned the store's name, while a senior Israeli official raised the matter with the state government.
"I plan to change the store's name very soon. There is tremendous pressure from the government and the Jewish community to drop the name," Manish Chandani, co-owner of the store, told AFP.
Chandani said he had not anticipated the shop would draw international attention and protests and that he had no intention of glorifying the German dictator.
The shop's name was chosen as a tribute to his grandfather, who was nicknamed Hitler for being a "very strict man", he explained.
"I will have to spend money from my pocket for re-branding the entire store. The logo, the hoarding and the business cards will be changed," he said.
"I was not aware of Hitler being responsible for the killings of six million people before the shop's inauguration. This time I will choose a non- controversial name."
Israel's embassy in India welcomed the store owner's decision, stressing that Hitler's name continues to evoke a sense of "pain and loss" among the Jewish community.
"I am happy that the store owner decided to change the name. I guess he realised that it was not the right thing to do," SAID Orna Sagive, consul general of Israel ;
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 (ADL), which fights against anti-Semitism.
Last week ADL warned that dictator's name was seeping into India's popular culture without any "appropriate context".
“It is a perverse abuse of the history of the Holocaust to name a business after one of the world’s most notorious mass murders and anti-Semites,” said Abraham H. Foxman, ADL National Director and a Holocaust survivor.
“Hitler’s name is seeping into India’s popular culture without any appropriate context. Clearly there’s a need for more education in India about the history of World War II and the rampant anti-Semitism that led to the mass murder of six million Jews and millions of others in the Holocaust.”
In a letter to the shop owner, ADL called his decision to name his store after Hitler “deeply offensive” and “an affront to the memory of the millions of Hitler’s victims.”
The League noted that the image of his storefront has been widely circulated around the world on the Internet.
Hitler attracts an unusual degree of interest in some parts of India, with his book "Mein Kampf" a popular title in bookshops and on street stalls.
Some Indians express private admiration for a leader seen as strong and decisive, while knowledge of the Holocaust and the other atrocities during the Third Reich is often patchy.
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.