Firstly many people confuse registering a company name with companies house with a registered trade mark – they are two entirely different things.
There are no restrictions on registering a company name other than you can’t have two companies with identical names. For example if you had a company name registered as “ABC Designs” then there is nothing stopping someone registering “ABC Designs (Glasgow)”.
If, on the other hand, your company/ brand name is a registered trade mark then if another company started trading is the same marked as you operate using a confusingly similar name then you would be able to take action to stop them. It should be noted that Companies House do not check whether the name being registered is protected by a trademark. The onus is on you to ensure that you regularly check for people who are potentially infringing your trade mark.
While there is no requirement to register your Brand Name as a trade mark, there are certainly advantages to be had from doing so. We would always recommend protecting your brand in as many ways as a practical for your business and that would include the use of registered trade marks. Conversely, we would also recommend that you should also check that there is no possibility of you infringing someone else’s trade mark before implementing a new brand name.