I am NOT a qualified legal professional, and laws (particularly copyright laws, which cross country boundaries) should really be advised by a lawyer.
But, since you asked, here is my opinion.
In most cases copyright applies to the CONTENT on a website and not the domain name.
You cannot copyright the domain name (as far as I know) although it is likely it can be registered as a trademark.
If your company name is 'similar' to another - which is protected by copyright - you may suffer from confusion; where consumers mistake you for them or vice versa. Unless your company name and/or the content of your site is identical to another you should not be in violation of any copyright laws.