UK you can be a sole trader, basically a person acting as a business. I believe there are some rules about how you legally present yourself (like in your contracts your name has to be "Bob Smith trading as Acme Widgets").
https://www.gov.uk/set-up-sole-trader
However, as the page says, you're personally liable if something went seriously wrong.
The alternative is to pay £50 to register as a ltd company, though there are costs in running one (£12.50 per year + doing your own accounts vs paying an accountant £200-£300).