You should register a business. You can register a sole proprietorship (not recommended for potential liability exposures to your personal assets.) or a limited liability company. Part of that process will require you to register a name (unless you do not mind running it as a numbered company - a number assigned to your company if you have not provided one). Having a company makes it possible for you to open a bank account in your business name and receive payments in that name.
Also remember you will require all kinds of insurance to protect yourself, including cargo insurance, unless your clients agree to cover their own goods (which rarely happens).
Good luck
