Cluster name in the node name

[mmartinello]

I installed a new Pulse instance ad added my first PVE cluster with the Quick Token Setup and the automatic agent installation:

Then I renamed the cluster name because I'll add a second cluster which hosts have the same names as the first one:

Anyway, in the Proxmox hosts list I continue to see the hostname only without the cluster name:

Could you help me to understand where I'm wrong, please?

What I want to achieve is similar to what I see in the demo instance (mock-cluster (pve1)):

Thank you!