The development of wireless industrial internet of things (IIoT) has facilitated the widespread deployment of dynamic digital twins across multiple factories and regions. However, the wireless communication between digital twins and their physical devices takes place over public channels, and the dynamic behavior of digital twins makes them susceptible to forgery and impersonation. As a result, data exchanged between digital twins is exposed to risks of tampering, fabrication and corruption. Moreover, real-time data sharing among a large number of digital twins incurs significant computational and communication overheads, thereby necessitating a secure and efficient cross-domain authentication scheme to ensure trustworthy identities and data integrity. To address these challenges, we propose ECroA, an efficient cross-domain authentication in dynamic digital twins of wireless IIoT. Specifically, we employ a distributed key management mechanism to establish trust across domains while reducing communication overhead. Additionally, we design an identity-based signature and pseudonym-based authentication scheme to provide conditional privacy preservation, ensuring secure data exchange without exposing sensitive data. To further enhance efficiency, we integrate signature aggregation and batch verification techniques, significantly reducing computational costs for large-scale cross-domain authentication. Performance analysis demonstrates that ECroA effectively enhances authentication efficiency while ensuring secure cross-domain authentication in dynamic digital twins of wireless IIoT.