Enter the income as other income so that it can be reported properly. If you are filing a Schedule C, then add it as income for the business.
The IRS will check your return against the income on the 1099 reported on your social security number. If you have a matching amount reported then they will accept this method of reporting the income even if you do not have a TIN/EIN associated with the income. You will still be paying the tax appropriately.