Under FAQ of the digital euro’s page Q9. How private would the digital euro be?, that they want it to be equivalent to cash when it comes to privacy.

The digital euro is designed to be able to function offline in a way that would offer users a cash-like level of privacy, both for sending money to other people and for making payments in shops. When paying offline, only the payer and the payee would know the personal transaction details of the payments made. Anti-money laundering checks would be carried out by the distributing payment service provider (PSP) during the funding and defunding process, just as it is the case with cash withdrawals and deposits today.

In the case of online transactions, the Eurosystem would not identify users making or receiving payments, thereby protecting their personal data, but PSPs would be able to identify users for the purpose of compliance with anti-money laundering rules.

I… am not entirely clear on the technical aspects of it, or if what they said can actually accomplish what they claim. However, it is a factor they are considering, however much you actually trust them aside.

I would be interested in an explainer, for sure, on how they actually accomplish any of this (assuming they deliver).