I think an anonymous bank account would be a bad idea for you.
Because you cannot prove that the account is yours if you are anonymous.
Apart from that banks are prohibited to do so. Every bank needs to abide with the international laws to prevent money laundering and funding to terrorist. You being anonymous would be able to do these kind of things, hence we got Know your customers legislation.
Banks can't do a lot of stuff but they still do it.
And of course they can't announce a product like an anonymous bank account but a prepaid card with a bank account number attached is essentially the same thing and they can sell that under the radar.