Jill Campbell has run the Isis Boutique in Malvern, Worcestershire, for seven years.
But she said people have been linking the store to Islamic State, which has killed hostages including British aid agency worker David Haines.
She said some comments have been "quite upsetting".
Some "very unpleasant" posts have also been made on social media about the shop, which is named after the river in Ms Campbell's home city, Oxford.
"I'm now in the position of thinking do I change the name or do I stick it out?" she said. "It's an unsettling time."
Ms Campbell plans to open a second boutique elsewhere in the country, but said she would "probably not" use the Isis name.
"I have absolutely no sympathy with these monsters in Syria and it is for very innocent reasons that we chose the name," she said.

Its annual report singles out President Donald Trump as an example of an "angrier and more divisive politics".
But it criticises other leaders, including those of Turkey, Hungary and the Philippines, who it says have used narratives of fear, blame and division.
The group also says governments are exploiting refugees for political ends.
The report, which covers 159 countries, cited a rise in hate speech across the US and Europe targeting refugees and said the reverberations would see more attacks on people on the basis of race, gender, nationality and religion.
It criticised countries that, it said, once claimed to champion rights abroad and that were now rolling back human rights at home.
"Instead of fighting for people's rights, too many leaders have adopted a dehumanizing agenda for political expediency," Salil Shetty, secretary general of Amnesty International, said in a statement.
"The limits of what is acceptable have shifted. Politicians are shamelessly and actively legitimizing all sorts of hateful rhetoric and policies based on people's identity: misogyny, racism and homophobia."
The group made special reference to Mr Trump's executive order last month that banned refugees and immigrants from seven mostly Muslim countries from entering the US.
It said Mr Trump put "his hateful xenophobic pre-election rhetoric" into action by signing the measure. The US president, who recently said he was the "least racist" and "least anti-Semitic person", is expected to unveil an updated order this week.
But Amnesty also mentioned Philippines President Rodrigo Duterte, Turkish President Recep Tayyip Erdogan and Hungarian Prime Minister Viktor Orban as leaders who were using the "us versus them" rhetoric.
"2016 was the year when the cynical use of 'us vs them' narratives of blame, hate and fear took on a global prominence to a level not seen since the 1930s," Mr Shetty added, citing the year when Adolf Hitler rose to power in Germany.
"A new world order where human rights are portrayed as a barrier to national interests makes the ability to tackle mass atrocities dangerously low, leaving the door open to abuses reminiscent of the darkest times of human history."
Kate Allen, director of Amnesty UK, criticised as "shameful" the recent decision by the British government to halt the scheme which allowed the entry of unaccompanied refugee children already in Europe, estimated to be 90,000.
The group also cited in its report:
The London-based group exceptionally launched its report in Paris, saying that France has seen an erosion of its rights in the name of security.
The French government says its measures, which followed a series of attacks in 2015, are necessary to protect the country.

The council plans to build at least 830 new homes in the Ancoats area of the city and neighbouring New Islington.
The plan will need to raise £1bn in the next 10 years and may need further investors to build the homes.
It is the first phase of the Manchester Life initiative and the homes will be rented out privately once built.
The plan will help the city meet its target to build tens of thousands of homes by 2027, according to Manchester City Council.
"The planned transformation of the eastern edge of the city centre is the single biggest residential investment Manchester has seen for a generation," said Sir Richard Leese, leader of Manchester City Council.
Abu Dhabi United Group is an investment company owned by Sheikh Mansour bin Zayed Nahyan and was formed to enable him to buy Manchester City Football Club in 2008.
It has also invested in other sporting assets including New York City Football Club, Melbourne City Football Club and Manchester City Women's FC.
A woman says she is considering rebranding her business because it shares its name with a Middle East extremist group.
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Politicians who have used a divisive and dehumanised rhetoric are creating a more divided and dangerous world, says rights group Amnesty International.
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Abu Dhabi United Group, which owns Manchester City football club, will invest in a plan by Manchester City Council to build new homes.