To me it seems you need some extended accesses to be able to manage Tags created in AJO by ordinary users. We see the need for change some names and deleting test Tags, but we cant do this else on out own created Tags. What kind of access do we need to do this on a "global" level, regardless of who created the Tag. The question is basically - what AJO access right can do this changes to Tags?
All users are able to access and browse the tags inventory, but tag management is limited to system and product admins
Only tags that are in an Archived state and are not associated with any objects can be deleted.
To answer your questions you should have Admin access to delete tags i believe.
https://experienceleague.adobe.com/en/docs/experience-platform/administrative-tags/overview
Hope this helps
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