Asking your offshore bank to issue you with a credit card is pretty much a sure way of having both your name and address given out to one of the large onshore credit card companies. Where many offshore banks do take a variety of technical steps to protect the confidentiality of their clients when it comes to credit cards, no solution has yet been found bullet-proof.
Lifestyle targeting - to determine your tax base!
In 2000, tax authorities in the United States (IRS) were granted access by a Miami court to thousands of Mastercard and American Express credit card accounts held by U.S. taxpayers in three offshore banking havens. The IRS claimed that they were using lifestyle targeting measures, looking for high-value purchases, airline tickets etc, in order to establish who was living beyond their means (their means as reported to the tax inspectors).
If you tell your offshore bank your actual residential address, forget about asking for a credit card. Never mind assurances about "confidential offshore payment clearing systems" and so on -- whatever protections your offshore bank puts in place, the fact remains that your credit card is going to be a part of one of the big global payment networks if it's to be of any use to you. Consequently, it can never be totally private.
Near-anonymous credit cards are possible but only where your offshore bank simply does not have the information that could enable onshore authorities to successfully identify you.
Near-anonymous credit cards are often arranged through the use of a nominee-administered offshore company and a bank that needs no more than a name and a signature for corporate cardholders. Note, however, that where the cardholder is also the actual beneficial owner of the underlying offshore company -- and mostly he/she is -- such a structure must be formed so as to successfully resist the leakage of personal information under any beneficial owner disclosure legislation.
But sometimes they just tell the Tax man (without telling you)!
You should also know that in at least one country widely touted for private offshore banking services, banks have a legal requirement to pass personal details (names and addresses) together with bank balances to the local tax office. There are no legal protections which oblige the local tax officer to keep this "non-resident" account information private.
There are many other circumstances where your name and address can find its way from your offshore bank into the hands of your home authorities -- and you might not even know it's happened.
Remember that to have an actual residential address attached to an account holder's name is simply invaluable to the bureaucrat who is willing to patiently wait until the supposedly private data leaks out from your offshore bank. Protect yourself accordingly, and be aware that you are under no legislative obligation to tell your offshore bank where you live. Those banks that do ask for utility bills or other proofs of residence are ignorant to issues of customer confidentiality.