I just tested both renaming and deleting/creating new cluster and this is reflected in NSX-T. I am also on 6.7U3 and NSX-T 2.5.
What I would check is the date of the last inventory collection in System > Fabric > Compute Managers and see if it has been updated. Also try to press the refresh button when in System > Fabric > Nodes > Host Transport Nodes (Managed by VCENTER).
Have you tried removing and adding vCenter again?