Open a private PO Box with a street address under the name of whatever, pay in cash and collect funds through USPS money order
Incorporate and create an online store and process transactions.
Use a third party billing company, like CC bill. You remain anonymous and theydo your billing and collection.
eta: whatever method you choose, make sure it is free from the threat of chargeback. And to further protect yourself from any allegations of fraud, make sure that you do not personally collect and credit card or banking details.
Personally, I'd go the money order & po box route, as you can pretty much conduct business anonymously. Especially if you have the mail forwarded to a second PO Box where you physically collect it.