In this paper, we describe the motivation, design, security properties, and a prototype implementation of NickPay, a new privacy-preserving yet auditable payment system built on top of the Ethereum blockchain platform. NickPay offers a strong level of privacy to participants and prevents successive payment transfers from being linked to their actual owners. It is providing the transparency that blockchains ensure and at the same time, preserving the possibility for a trusted authority to access sensitive information, e.g., for audit purposes or compliance with financial regulations. NickPay builds upon the Nicknames for Group Signatures (NGS) scheme, a new signing system based on dynamic ``nicknames'' for signers that extends the schemes of group signatures and signatures with flexible public keys. NGS enables identified group members to expose their flexible public keys, thus allowing direct and natural applications such as auditable private payment systems, NickPay being a blockchain-based prototype of these.