Sorry I only have vague-from-memory advice. I'd think your simplest option would be to register "The Sphynx Corporation" or similar and set up a bank account and regular PayPal account for that.
Other gateways I've seen, e.g. WorldPay, generally say "you're making a payment to X" on the payment page and I don't know of one that allows enough rebranding of the page or payment-accepted email to eliminate that. However nowadays the customer will often get redirected to a 3D-secure systems (VbV etc.) that will also display a payment-to line. So you won't get away completely without displaying a name so you're going to need a bank account or merchant account somewhere down the line under a different name. Chances are that'll have to be registered to some legal company: that'll mean some small cost maintaining the company every year (e.g. filing accounts) and there will be mechanisms to trace that company back to you (e.g. Companies House in the UK) but at least it won't publish your name outright.
You can go down the payment integration route and accept the card numbers directly on your website, e.g. using PayPal Website Payments Pro or SecureTrading. You then you can control what appears around the form but I still think you'll need a merchant account with a bank to use these services and again a name will appear on 3D-secure systems and on the consumer's credit card bill.