The business name I have chosen for my online retail store is very similar to one that is based in the US. They have a bricks and mortar as well as selling a host of items online worldwide. I will only be selling 1 category of what they sell. I have bought the .uk domain name which is along the lines of Thebusinessname.co.uk. Theirs is shopbusinessname.com There is no UK company registered on companies house or trademarked that name and I do have the .co.uk and .com websites. Would they be able to make me change my business name further down the line? How do I stand legally? Are there any other considerations to running an online store with a similar name? Are there any examples?