Sweet Jesus ice cream has faced condemnation since it began in 2015, but criticism has recently got worse, some accusing the company of being "satanic" and demanding the company change its name.
A woman wrote on Activist Mommy blog that "Sweet Jesus", is a "blasphemous expression" that someone might say when enjoying the shop's ice cream and has nothing to do with someone's love for Jesus Christ.
She added: "This is immediately apparent by their logo, which features an SS style "S", popular among equally blasphemous and satanic metal bands of the 70s and 80s, and an upside down cross.
"So they want to make quite sure we know they are in fact, not Christian, and that the entire marketing concept of their company is to mock the name of the Lord Jesus Christ."
A Citizen Go petition, which has more than 9,650 signatures, asks the brand's founders, Andrew Richmond and Amin Todai to apologise for mocking Christianity and to immediately change its name and all its branding.
It adds: "Sweet Jesus is all about trashing Christianity and mocking the saving work of our Lord Jesus Christ. This is deeply offensive and an outright attack on the Christian community of Canada!"
A second petition on Change.org said "It is time for Christians to take a stand against the Anti-Christ agenda" and urged Christians to boycott the company.
However, the founders of the brand have not given in to the backlash, but said their intention is not to offend Christianity.
Richmond said in a statement that the company "was created from the popular phrase that people use as an expression of joy, surprise or disbelief".
He added: "We found this firsthand, often using it while testing new items in our kitchens.
"We are conscious of the fact that, to some, our name can be off-putting. That fact is something we struggle with because we sincerely do not wish to give offense or show disrespect in any way toward anyone's personal beliefs. Neither is it our intention to be exploitative or flagrantly provocative."
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