Identity verification in Data Spaces is a fundamental aspect of ensuring security and privacy in digital environments. This paper presents an identity verification protocol tailored for shared data environments within Data Spaces. This protocol extends the Grant Negotiation and Authorization Protocol (GNAP) and integrates OpenID Connect for Verifiable Presentations (OIDC4VP) along with support for Linked Verifiable Presentations (LVP), providing a robust foundation for secure and privacy-preserving interactions. The proposed solution adheres to the principles of Self-Sovereign Identity (SSI) to facilitate decentralized, user-centric identity management while maintaining flexibility through protocol negotiation. Two alternative interaction flows are introduced: a "Wallet-Driven Interaction" utilizing OIDC4VP, and a "LVP Authorization" model for fully automated machine-to-machine communication. These flows address critical challenges encountered in Data Spaces, including privacy, interoperability, and regulatory compliance while simultaneously ensuring scalability and minimizing trust assumptions. The paper provides a detailed technical design, outlining the implementation considerations, and demonstrating how the proposed flows guarantee verifiable, secure, and efficient interactions between participants. This work contributes towards the establishment of a more trustworthy and sovereign digital infrastructure, in alignment with emerging European data governance initiatives.