ISO 27001 does not prescribe the information to be included in an inventory of assets, so organizations can define them as best they fit their needs.
Both alternatives have disadvantages and advantages:
by using the owner’s name, it is easier to identify who to contact, but the inventory will need to be updated every time the asset’s owner changes.
by using the owner’s role changes in the inventory, you won’t need to update the inventory if a new person is in charge, but the inventory will become less personal, and you will need additional information to identify the person.
You also can use both information to write your inventory. The turnover rate in your organization will help you assess which approach is better for your organization