Read up on Cyber-Squatting Law
http://www.nolo.com/legal-encyclopedia/c...
There is cause to have a site shut down if the name misleads people to believe it represents some well known company.
One for example get the free domain name Nike.co.cc to sell counterfeit sneakers, which would damage nike.
In te early days of the internet domain name speculators were buying big corporation names like Pepsi.com before the businesses got started in the internet, holding the name hostage for big money, this is one practice the law is designed to stop.
If you used a trade name that has been in existence longer than you have and is registered under international trademark law, you may be forced to give up you web site. For example, if you are using www.bmw.com and the other company was BMW (the car company) they could have rights to www.bmw.com. The only way you will know is to get a trademark lawyer of your own.
what are they saying the problem is? - I would tell them F* you - if they had any legitimate claim to the name, they would not have waited 2 yrs to contact you - I wouldn't even respond to them - emails from a "lawyer" mean NOTHING - all REAL legal claims are done on paper - see if you can block their email address
It's meaningless if they don't have it trademarked and no other reason for lawsuit