No, sole traders do not need to register a company name. You simply need to provide HMRC with a business name when you register online as a sole trader. You can trade under your own name or a dedicated business name, it’s entirely up to you, but you must follow certain rules when choosing a name.
Whilst not a legal requirement for sole traders, registering a company name is an effective way to protect the name of your business, so this is something you may want to consider. By doing so, no one else will be able to register a company using the same name.
If this sounds like something you wish to do, you will have to register a limited company at Companies House and then contact your local Corporation Tax office to tell them that your company is dormant (not trading).