They have launched a campaign to share what they are going through and to pressure media to switch from ISIS, which stands for Islamic State of Iraq and Syria, to ISIL, which stands for Islamic State of Iraq and the Levant. The organization itself is using the name Islamic State, but that has not been adopted by most Western media organizations.
What to call the group and how to translate its Arabic name into English have been matters of debate.
What is not in doubt is that women named Isis now have a name associated with militants responsible for enslaving women and grotesque acts of violence, including the beheadings of American journalists and British aid workers.
At the forefront of the "Save Our Name" campaign is a Miami woman named Isis Martinez. In a YouTube video she says that the last few weeks have been "incredibly challenging."
"My name is Isis, I love my name. Or so, I loved it a lot more before," she says.
The last straw, she says in the video, came when she was at a hospital and the intake worker asked how to pronounce her name.
"Her face showed such incredible sadness for me and she said she felt bad for me and proceeded to ask if I had a middle name I could go by instead," says Martinez.
Petition created to 'Save Our Name'
Martinez was named after her mother, who, like many other women named Isis, was named after an Egyptian goddess.
"I will not and cannot change my name and neither should the thousands of other women who share this beautiful name," she said.
Martinez created a "Save Our Name" Facebook page that links to a petition asking media to stop using the ISIS acronym. It's also serving as a platform for people to share their stories.
"I cringe every time my sweet baby's name is mentioned in the media as an acronym to a fanatical terrorist group," one woman wrote.
"I have spent many years building a good name for myself and being a positive role model for women in general. It is very disheartening to see the name Isis defamed and used in such an ugly light in just a matter of weeks. My parents named me Isis because of the strong, positive connotation this name carries," wrote Isis Ardrey, a woman in Toledo, Ohio.
A father in Portland, Ore., told a local news station that he's considering a class action lawsuit against media companies. His three-year-old daughter is named Isis.
"You want to call her name and you get weird looks now and that's not acceptable," David Emami told KATU news channel. "I don't feel like we should be paying the price for the inaccurate use of an acronym."
Isis is 'a beautiful name'
"It's a beautiful name," Emami said. "She's named after an Egyptian goddess. To see it be misused in such a form, it's gut-wrenching, it hurts."
Martinez said sharing a name with the group is taking an emotional toll, but also a financial one, since her line of work in holistic health involves working with clients.
While she's not going to change her name, the animated television series Archer has dropped its use of ISIS, which was the fictional spy agency at the heart of the show for the last five seasons. It stood for International Secret Intelligence Service.
The show's creator Adam Reed told the Daily Beast that he and the executive producers had hoped the jihadist group ISIS would become irrelevant, but it has only become more prominent and continues to dominate the news cycles.
In light of how ISIS has taken hold in mainstream language, they made the decision to scrub ISIS from the show, and the characters will work for the CIA instead in the upcoming season. They still have a problem however: what to do with piles of Archer merchandise with ISIS branding on it.
"I guess that's all going to a landfill somewhere," Reed told the Daily Beast.
Women named Isis, however, aren't giving up on their name so easily. The petition has so far collected more than 37,000 signatures.