Privacy is one of the most important design features of the digital euro.
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 paying in shops. When paying offline, only the payer and the payee would know the personal transaction details of the payments made.
For online digital euro payments, privacy would be implemented so that the Eurosystem itself – the issuer and payment infrastructure provider – would not be able to directly connect transactions to specific individuals.
From their FAQ:
Further reading link they provide: https://www.ecb.europa.eu/euro/digital_euro/features/privacy/html/index.en.html