The European Central Bank (ECB) has launched a project on the introduction of the digital euro as another form of digital central bank money (CBDC), in which it intends to investigate the benefits and negative consequences that could result from its introduction, taking into account the architecture of the system and the type of technology on which it is based. Centralised and decentralised digital euro architectures in the form of tokens or in the form of deposits will be considered. Since a centralised architecture would have negative consequences, including a greater threat to privacy and data protection for citizens' transactions, a decentralised system is mainly examined. In this paper, the protection of citizens' privacy and data is examined from the perspective of the system architecture and the nature of the fiat money system, i.e. the digital euro. From the analysis of the report of ECB on the digital euro adoption project, as well as from academic works and researches on this topic, it can be concluded that for citizens, one of the most important features of CBDC is a high level of anonymity of payments. Therefore, it would be optimal if they could use the digital euro to make payments of smaller values in the form of tokens and higher digital euro payments in the form of deposits, which would allow the digital euro to compete with cryptocurrencies in terms of the anonymity of payments. To avoid the centralisation of the financial system and the serious consequences of possible cyberattacks, it is also desirable to create a hybrid system in which citizens would have direct claims on the central bank and commercial banks would offer them account opening and management services. If such a model would be too expensive, then it would be better if it were at least decentralised.