Well, it is hard to say from info provided whether the goods and/or services you and they provide would be considered related. It is possible.
Further, while they present one possible conflict there may very well be others that precede both of you and have prior use for the mark in question. The only way to know is to have a proper clearnace search conducted (see link on TM due diligence below).
But if they are in completely different goods or services this may not pose a problem (think Delata Airlines vs Delta faucets).
I would not rely on your own ideas about this, but have a proper clearance search and USPTO filing done. You may want to discuss this over with a TM lawyer before doing anything. I will link you to some general helpful info below and most of us here, including myself, offer a free phone consult.
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This is an issue of trademark, not copyright.
Don't expect a definitive answer that an attorney will stand behind on something like this in a forum full of short, free answers. This will take serious analysis, and likely research, to see if you are "too" close.
Very, very roughly, if the names and types of business are similar enough that someone is likely to assume a connection, you can't do this.
Being even "close" is likely to be buying expensive litigation. If you want to go ahead with such a name, pay a trademark attorney for opinion before moving forward.Ask a similar question