With trademarks, what we worry about is Likelihood of Confusion. That is, is your name confusingly similar to someone else’s name, being used for similar goods or services?
The other thing we worry about is whether someone might assert that your name takes unfair advantage of their brand image or awareness. And if they can prove that you have done this knowingly, any damages they have been awarded (which you will have to pay) will be tripled for this "knowing infringement."
Your best course is to find name that you love, that is not similar to the name anyone else is using for similar goods and services.
Multiple users of the same name, even if they are identical, can coexist if their goods and services are different and unlikely to be confused with each other, for example the Eos car and the Eos camera.
Our algorithm does much of the work of figuring this out for you, showing the most troubling hits in the center, of your visualization, with progressively less threatening (but still noteworthy) name users on the outer ovals. When reviewing the hits found in your visualization, you should be most worried about hits with the same or similar names, and the same or similar goods, which typically will be displayed closer to the center of the graph.
A name with few nearby hits, or none, is generally a better prospect than a name with many.