What is the role of the process owner?

Answer:

A Process Owner is a person who is given the responsibility and authority for managing a particular process. A process owner is responsible for the design of the process, how it is carried out, how it interacts with other processes, and how it is measured. Process owner identifies process documentation and training requirements, identifies risks and opportunities with the current process. Of course, this responsibility is an ongoing task.

For more information on the process approach, you can see the following article. This article is written for ISO 9001, but the process approach described is also fully applicable for ISO 13485.
ISO 9001: The importance of the process approach https://advisera.com/9001academy/blog/2015/12/01/iso-9001-the-importance-of-the-process-approach/