This paper presents a protocol for Identity Management in Industrial IoT enabled devices, that is based on the principles of Self-Sovereign Identity. The Industry 4.0 transformation has led to the Industry sector digitalization and one of its major challenges is to uniquely identify the Industrial Internet of Things unattended devices. The digital identity management must allow increasing the security and control, and it has been evolving towards a model where the device acquires the responsibility for managing its own data through Self-Sovereign Identity. This paper studies why the Self-Sovereign Identity approach is suitable for the industrial IoT particularities, properly justifying its use. Furthermore, it analyzes the actors and roles involved in an industrial identity environment, and it addresses a protocol that defines how data should be exchanged over an Hyperledger Indy public permissioned Distributed Ledger Technology network as Sovrin. The paper applies the proposal to a reference use case, filling the gaps that are not currently specified in the literature for a successful Industrial Internet of Things identity management operation.