In Europe you'd get issues with accounting, both in terms of figuring out value added tax, in terms of your local tax authority asking uncomfortable questions why you have expenses without valid invoices (and yes, an invoice has to show who is invoicing). The first probably isn't an issue in the US, I'm not sure about the second.

You could try to set up a company to hide your identity, but how well that works depends on the jurisdiction (in many places it's trivial to figure out the director of a company).