You can setup an offshore company almost anonymously to use this term. A Seychelles company is actually offering you exact this. Since there is no public registry in the Seychelles to lookup any ownership information this entity will protect your privacy 100%.
For banking and credit card processing it's going to be more difficult. A Cyprus company will, if opened in the name of the Seychelles company protect your privacy too, it will require several court orders to gain access to any information about the account and company if there is no evidence of fraud or criminal activity that apply to local laws in the︀ respective countries.
With the credit card processing it's almost impossible. You will need to use︁ service like Payoneer, BitCoin / BitPay or Neteller, skrill to get that and then you︂ need some special documents to get this sorted out. A normal credit card processor will︃ most often not work. Except you find a 3rd party payment processor that is new︄ to all of it. So you will have the risk to lose your money because︅ they most often get out of business after a few years and sometimes even faster!︆
