If your company is a real, viable company with a bunch of employees, it is already time for you to consult an Intellectual Property attorney about this case. You may get useful advice here but it's well worth your while to pay for the real thing. The attorney should be able to figure out pretty quickly whether you have a trademark infringement case.
That said, your name is most protected if it has no obvious connection to your product, for instance if your product is a lawn sprinkler called "Hugh's Lawn-Bee". There's a continuum with very arbitrary names at the most protected end, and very generic or descriptive names, such as "The Patented Lawn Sprinkler System" at the least protected end.
But get a lawyer.
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