Which process is responsible for managing relationships with vendors?

Change Management controls the lifecycle of all changes and is not concerned with vendor relationship management.

Service Portfolio Management manages the full set of services the provider offers or plans to offer, not vendor relationships.

Supplier Management is the ITIL Service Design process that manages all suppliers and the services they deliver. It maintains supplier policies and a supplier and contract database, and ensures suppliers meet contractual commitments. Its primary goal is to obtain value for money from suppliers and support the delivery of end-to-end IT services.

Continual Service Improvement focuses on identifying and implementing improvements to IT services and processes, not on managing suppliers.