If you received a 1099-Misc for contract work and the amount you received is entered in Box 7, Non Employee Compensation , you are considered to be self-employed. Your business can just be your name, address, and social security number.
TurboTax will prepare a Schedule C for Self-Employment to be included in your tax return. You can then deduct any expenses associated with earning this income (mileage, supplies, etc.) and will be assessed self-employment tax.
If this was a one-time project and you don't plan to do this type of work in the future, you could ask the Payor to issue you a corrected 1099-Misc with the amount in Box 3.
Here's some tips for self-employment you may find helpful.
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