You should choose a business name. As a sole trader you do not have to register a business name but you need to publicise a fixed point of contact so that people connect the business name with you in your capacity as a sole trader (eg a statement on your business stationery: "Mary Brown trading as 'Heaven Scent Cosmetics', 123 High Street ...etc").
As soon as you can after starting your business, you must register for self-assessment with HMRC.
For more information on your responsibilities as a sole trader read Running your business.