If the other company has a registered trade mark in the class which covers the goods you sell they can prevent you from using that name. However, if they have never used the name, or if it's only slightly similar and not confusing, you may be able to keep your use of the name. If neither name is registered it would be a case of proving passing-off. You should take legal advice, check their mark is registered and try to agree a settlement or negotiate a licence from them to use the name. Note that unjustified threats of trade mark infringement are against the law under the 1994 Act, so if they have no grounds you could obtain a court declaration that you have the right to use the trade mark you use.
Singletons are specialist intellectual property solicitors.
If you have a legal question which you would like answered then please write to the Editor, Inventors World, clearly marking your envelope 'Inventors Legal Problems'. We regret that, due to the complex nature of Intellectual Property Law, we cannot enter into personal correspondence, nor name correspondents.