Do they have a trademark on that name in their country, any other countries, or your country? IIf so, you have to worry about where you use their trademark.
Depends on the country and type of business you are dealing with. Your products/services are being traded with in country or locally then their will be no trouble for the company. However, if your company involved in trading on different parts of the world and other company too then there will be clash between your and other company dealing same products/services with same name at the same location.
I think the question everyone should be asking you first is, why are you naming your company exactly the same as an existing company in the same industry but in a different country? I mean, is the name that good? and if it is, wouldn't that be a problem for the other company and you as well when customers start getting confused and potentially think that both companies are the same? If you still want to do this for some reason that I will not understand, then the easiest way to find out about this is to ask a trademark lawyer.