In the age of transparency it's getting very hard for a good bank to open up an account for you anymore. Number account went away with 911 attacks mostly as Patriot act made sure that banks all over the world can't open numbered account anymore for security reasons.
Interesting, thanks. How about payment cards? Would the cards associated with such accounts have the number as "name" that one can punch into the "card owner" fields, or are just normal cards with account holder name?
Banks offers this services, if you like it or not. They offer it to a clients, who they know very well. This services are not offered for unknown or new clients. Swiss bankers are not naive. But they love money. So they try to provide as many privacy and services to their clients as they can. Privacy was something what was available for all in the past. It is available for wealthy, only. If you believe, that there are just the same bank services for wealthy people like for all other average people, you are naive. Not a swiss bankers. Wealthy people received higher level of services and privacy all the time. It is the same for hundreds years and this will stay for next hundreds years. If you believe in that socialistic bullshits about total transparency, you should not swhich off CNN for all the day. Just socialists believe, that people are equal. In reality - people are not equal. And services for wealthy people exists. Bank is a business. Nothing else. They has to earn money. They has to understand ration of risks and profits as well as ration of income and costs. If they want to have a wealthy clients, they have to provide them a services, which are providing a level of privacy as this people require and need. Open your eyes. Do you really believe, that services for poor average people are the same as services for wealthy people? This is just a wet wish of all socialist. Socialist believe, that all wealth of all people around a globe should be transparent. Rich people does not see is this way. They are ready to pay for high level services and they value their privacy very high.Your instructions miss out on something important. Swiss bankers are not that naïve any longer as you describe them here.
If you are wealthy and have millions already I'm sure you don't have them laying under your bet so a quick call to your current bank will open an account and deposit box in Switzerland if that is what you want.
The entire problem to involve banks in your operation is that if you are into black money and money laundering and you engage banks in such activity one way or another your will go to jail some day. As @Martin Everson and @Sols and a few other people pointed out already, authorities will monitor maybe 5, 10 and even 20 years then they will hook as a shark from the deep.
On the other hand, if you have millions already, I'm sure you don't sit behind a screen on a public forum to find ways to transport your money! That again makes it irrelevant to post about possible constellation that costs thousands of EURO's and which only purpose is to increase a users post count and reputation to get users contacting you.