At least one processing device is configured to register a logical storage device of a storage system for a first set of paths associated with a first access protocol using a host identifier, to send a first reservation command in the first access protocol over each of the paths in the first set of paths, to register the logical storage device of the storage system for a second set of paths associated with a second access protocol using the same host identifier used in registering the logical storage device for the first set of paths, to receive an additional reservation command in the first access protocol, and responsive to receipt of the additional reservation command in the first access protocol, to translate the additional reservation command to the second access protocol, and to send the additional reservation command in the second access protocol to the storage system.