True bu you can still hide your identity and in countries with strict bank secrecy you will not have the beneficial owner information released to anyone.
The Swiss have the best reputation for maintaining confidentiality of information pertaining to their clients. However, if you've ventured into other areas of this forum, a news item was posted concerning a Swiss bank
agreeing to release names of clients to the US government.
You can hide your identity from the general public but not to bank personnel. Swiss banking laws require at least one bank personnel meet the beneficial owner in person at least once (that is, if I'm not mistaken). So, obviously, totally anonymous account isn't possible.