To have a legal agreement with anyone using business name you need legal ground to use that name. Short answer is yes you need to register your business.
There are of course the thing that if you will get paid you need a business to pay taxes for that profit but you can become self-employed which will be easier at the start than starting a LLC (Limited Liability Company).
On the other hand starting a LLC will give you more financial independence in cases when things don't go as planned as you can only lose money invested in that business while all your personal items (house, car, money and other belongings) are safe.