ITIL and ISO 20000 overlap quite a lot. Usage of ITIL processes for ISO 20000 implementation depends also on the detail of the implementation. Ownership of the processes depends on how many employees your ITSM organization have. Ideally, every process would have different owner. But, process owners can be combined.
Here are more details:
ITIL and ISO 20000: A Comparison https://advisera.com/20000academy/knowledgebase/itil-iso-20000-comparison/
Defining roles and responsibilities for ISO 20000-based IT Service Management https://advisera.com/20000academy/blog/2017/10/18/defining-roles-and-responsibilities-for-iso-20000-based-it-service-management/
What ITIL roles can be combined in one person? https://advisera.com/20000academy/knowledgebase/itil-roles-can-combined-one-person/