Registering a Sole Trader business will not protect its name.
It is quite common for people who want to be a Sole Trader to register a limited company with their preferred business name.
This makes sure that the name is reserved on the Companies House register and that no-one else can register the same name. It also gives you a fixed point to show you have asserted your rights on the name which can be useful if you ever get involved in a trade mark or passing off case.