The group filed a lawsuit against the owners of the online store that sells firearms and other accessories including flowers.
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The rock band said the store, Texas Guns And Roses, is causing confusion and damaging their reputation.
The group, that has sold millions of records, is concerned that fans could think the band is somehow connected to the online shop.
According to the lawsuit, the website owner, Jersey Village Florist, registered the name without the band's approval.
Now, the band wants the store to stop using the name.
There are differences between the two names. However, the rock band said any damage done by having similar names is permanent.
The attorney for the online store, David Clark, said he does not see the similarities.
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"There is no confusion between the brands. The band and its attorneys have admitted that. We will kindly respond as needed, and we will be fighting back," Clark told ABC13 in a statement.
Clark also pointed out that one trademark is for music and entertainment, while the other is for retail and metal safes.
He said there are no plans to shut down the online website.
Clark would not discuss the next steps, explaining the company has yet to be served the lawsuit.
ABC13 reached out to attorneys for the rock band but have yet to hear back.