how do you register a business name?

how can you register a name for a small business in the uk and how much do is cost to register, also if you register a name can someone else make a new business and use the name that you have resisted

to register go to companies house website

Other business may have a similar name
but as long as they are not in your town/city
they are unlikely to have an affect,threaten or impact on your business

This is a requirement of the Registration of Business Names Act 1916.
It was initiated during the first World War when there was some public interest in identifying businesses that were operated by foreigners. It is not necessary to register under this Act, if the business is operated under the actual name of the person trading, or under a name assumed on being elevated to the peerage. If registered name is that of a Company another company may not use the same identical name, but could add some detail to identify it as a different business.

Might be that Business Names registration is still made to Registrar at Companies House.

You only register your business name if you set up a limited company. Look at the Companies House website for more information. You can do it for under £50 yourself.

Otherwise, the only registering of a business that's required is informing Inland Revenue within 3 months of setting up your business.

If you've registered your name at Companies House, no-one else can set up a limited company with the same name. This doesn't stop someone trading with a very similar name. If they're in the same area as you, they could be held to be trying to pass themselves off as your company, which may be actionable. If they're a couple of hundred miles away, you're unlikely to know about it and it's unlikely to affect you.

Speak to your local Business Link for lots of free help about the best way of setting up your business.

Good luck!