It is OK to not have a business name when you are working as an independent contractor for a delivery company, but you will need to enter a business code for your Schedule C business.
If you are using TurboTax Online, the program will help you get the correct code entered based on some of your other inputs. This TurboTax help article will give you more details: What's the Business Code used for?
If you are using TurboTax Desktop, there is also a lookup tool that you can use. For a delivery driver, you could enter code 492000 for Couriers, Local messengers and local delivery. Or enter 999000 as another option.
Do not stress over getting the code exactly right. It does not affect your tax return.
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