Is this other company in the same or similar business as you so that there might be a risk of confusion? - if there is no risk of confusion whatsoever then you can both establish separate independant ownership.
If you have prior use and there is a risk of confusion, then you may be in a position to bring an action for 'passing off' under the common law.
However, the situation would be clearer, and your position stronger, if you had trade mark registration for your name (assuming the name is registrable as such).
Registration of a name at Companies House or as a domain name gives no protection, it simply stops anybody registering the identical name in the same way.
Trade mark registration, however, protects all forms of commercial usage of a name, whether as a company name, business name, product name, shop name, domain name, website name, in fact any form of commercial activity under the same or similar name which may lead to confusion.
Usage alone of a business name or identity affords a certain amount of protection under the common law against passing off . However, this is not only more limited in scope but legal actions for passing off tend to be both more expensive and more uncertain in outcome as well as requiring evidence of likely confusion.
On the other hand unlike protection for passing off - trade mark registration not only gives immediate national coverage but it is not necessary to show that confusion is likely for trade mark infringement to be established in the case of identicality.
Accordingly, if for example you only trade in Cornwall but have your name as a registered trade mark, and someone else then starts up in Scotland using the same name for the same kind of goods/services as you have registered for, then they can be guilty of infringement even though the geographical separation means that there is no confusion.
Trade mark registration can thus be both a potent weapon and a strong shield to protect your business name and identity. It can also increase a businesss value by strengthening its appeal to investors or licensees.
Our website at
www.verymark.info has a lot of free information on trade marks, copyright, designs and patents, or you can email us directly (see link below) for further help.