In academia and at central banks, central bank digital currency (CBDC) is increasingly being researched due to the continuous decline in cash payments and the emergence of private stablecoins such as Libra. While CBDC offers various advantages for central banks, sensitive transaction and holdings data of individuals and users need to be protected. This paper analyses how privacy in payment is being discussed in CBDC related literature and pilot projects of central banks. Central banks rarely identify privacy as a key requirement in the development and implementation of a CBDC. Instead, anonymity is seen as one possible feature of a CBDC that could hinder know-your-customer (KYC) and anti-money laundering (AML) compliance of banks. In pilot projects, different techniques and solutions have been proposed to achieve varying levels of privacy for users. A comprehensive framework on how best to achieve privacy in retail CBDC is needed. Such a framework should consider the differing underlying design aspects of a CBDC and the use cases for which the CBDC is to be developed.