If they can show that the two names are confusingly similar, and they can show that you have no legitimate interest in the domain and have adopted and are using the domain in bad faith, they can have the domain transferred to them. That is a separate issue from whether or not trademark infringement exists. You have not provided enough information about your business and theirs and what the two names are, so that no specific evaluation can be made; however, what you are asking goes beyond what can be handled via this site so I suggest that you contact a trademark attorney who also handles domain name disputes.
Answered on Mar 20th, 2015 at 12:10 PM