Self-Sovereign Identity (SSI) has recently emerged as an identity and access management framework based on Distributed Ledger Technology (DLT) that enables users or organizations to control their own data. The Open RAN (O-RAN), on the other hand, provides a framework for sharing infrastructure-related data between users and mobile network operators (MNOs). By leveraging SSI, O-RAN can benefit from decentralized and secure identity management that enables a more transparent, efficient, and user-centric network ecosystem. This paper examines identity, inventory and configuration management, and authentication of users or MNOs for a resource sharing scenario in an O-RAN architecture. At the end of the paper, we explain the potential limitations and possible solutions for applying SSI to improve security, privacy, trust, and interoperability in O-RANs.