In the API output we can see that only display name has changed. Path and id did not change.
GET https://<nsx-manager>/policy/api/v1/infra/tier-0s/
"id": "T0-Test-01", "display_name": "T0-Test-01_rename", "path": "/infra/tier-0s/T0-Test-01", curl -k -u admin -X GET "https://localhost/policy/api/v1/infra/tier-0s/"VMware NSX
For tier-0 and other objects of NSX policy id is an immutable attribute.
Create new Tier-0 with desired name to change id of Tier-0.