ISO 20000 Design and transition of new or changed services

Answer:
Design and transition of new or changed services is responsible (in scope of the SMS - Service Management System) to manage any changes on existing, or introduction of new services. In your case, I rather see that you'll have changes on existing services. In scope of your change management (e.g. in your policy) you should define which changes are introduced using design and transition process.
If you have Design and transition process in place, evidences that you can show to the auditor could include:
- specification
- service requirements
- test plan
- transition plan
- risk assessment
- service acceptance criteria, etc.

Here are few articles that could help:
ITIL Service Acceptanc e Criteria – keep control in your hands https://advisera.com/20000academy/knowledgebase/itil-service-acceptance-criteria-keep-control-hands/
ITIL/ISO 20000 Service Level Requirements – Ensure you deliver what the customer asked for https://advisera.com/20000academy/blog/2017/03/21/itiliso-20000-service-level-requirements-ensure-you-deliver-what-the-customer-asked-for/
Design and transition of new or changed services in ISO 20000 https://advisera.com/20000academy/blog/2014/07/15/design-transition-new-changed-services-iso-20000/