It asks for a company name on a schedule C but I am not employed through a company or own my own company
Yes. You DO have a business.
Income reported in box 1 of form 1099-NEC is self-employed income. You are considered as self-employed and in IRS terms, are operating a business doing what you do to earn the income reported on the form 1099-NEC. You enter your form 1099-NEC in TurboTax and TurboTax will populate a Schedule C after you enter all your information. You can deduct any expenses you paid related to this activity (such as supplies, car expenses, etc.)
Self-employed income is subject to income tax AND self-employment tax (calculated at 15.3% on 92.35% of net self-employed income).
You do not own a business in the common meaning of the word. So in TurboTax answer that you use the cash method, that you do not have an EIN. You use your own name as the business name and your personal address as the business address. You can use 999999 as your business code.
You’ll need to use TurboTax Deluxe (or TurboTax Online Premium if you have expenses to deduct), or any version of TurboTax CD/Download.
You can read this TurboTax article for more information.