In my course (that I'm still writing) called "What is the Service design process?" I mention 8 processes:

1. Service Design Playbook by British Columbia Government Public Service

2. Civic Service Design Process

3. Service Standard by the UK Government Digital Service

4. Digital Service Standard criteria by the Australian Digital Tranformation Agency

5. Service design and delivery process by the Digitial Transformation Agency of the Australian Government

6. The Scottish Approach to Service Design (SAtSD)

7. Project X's innovation model by Innovationsguiden

8. Colour-in City design process