OK there are a few understandable misunderstandings here as to how intellectual property works (copyright etc).
Firstly just because a company has a registered name (link to Co House is
Companies House) DOES mean that you cannot have a company similarly registered BUT IT DOES NOT MEAN that you cannot use that name as a sole trader (for example). You may, however, encounter problems with what is called "passing off" if someone else objects to your use of the name. This is often likely to happen if you are both in the same industry (as in your case) and are local.
Secondly, copyright isn't anything that you can register (or necessarily that you need to declare with that funny (c). This post, for example, is copyrighted to me automatically- I suspect Salon Geek's terms probably say that we waive our copyright in this material to allow it to be copied etc.
Thirdly, you can register a company online or a company agent, solicitor or accountant can do it for you. I can't recommend strongly enough however that you consider if being a company is right for you. I have a factsheet on this which I am happy to send but guidance is on most accountancy websites. There are so many factors other than simply registering a name and as I have explained above having a company name DOES NOT give you exclusive rights to it.
Lastly (sorry to go on!) if you have a brand (either its a name or a logo for example) then the best recommendation I can make is to have that trade marked. That WILL give you the protection you are after.
I hope this helps!