Cloud computing is an evolving paradigm that is frequently changing the way humans share, store, and access their information in digital format. While cloud computing offers tremendous benefits (e.g., efficiency, flexibility, and reduced costs), it also brings both security and privacy challenges. Although cloud security has been extensively defined and developed, privacy protections in cloud environments are often described in abstract or vague language, which makes it difficult to interpret and implement. In this study, we propose an initial approach of developing a privacy glossary for cloud computing that provides a consistent and comprehensive set of terminologies for cloud privacy. We believe that this systematic and structured privacy glossary could serve as a first step towards implementing requirements for privacy protections in cloud computing, as well as providing more effective and consistent language in cloud privacy to researchers and professionals in the future.