Depends on which company used the trade name first and where in the country the two do business.
A trade name is not the same thing as a trademark. Many companies throughout the country have the same trade name. That's a problem only if the companies are in the same state or if the trade names are also used as trademarks and they are confusingly similar and brand related goods or services [as your's do].
As far as domain names, so long as you have a legitimate reason to use the domain you registered -- and you do -- then you it cannot be taken away. UNLESS, of course, if the other company sues you for trademark infringement for using your trade name as a trademark as its confusingly similar to the other company's.
In short, there are way too many variables to tell you if you "will be in trouble."
What IS clear is that if you use your trade name as a brand to sell whatever it is that you sell, then you certainly need to discuss this situation with a trademark attorney. The last thing you need is to create marketplace buzz and then be forced to change your name.