How do I correctly use the ansible hostname module?

You can create a new variable for each of the servers in the inventory like

[k8s_kvm_vms]
server1 new_hostname=centos1
server2 new_hostname=centos2

Playbook:

---
- hosts: k8s_kvm_vms
  tasks:
  - name: "update hostnames"
    hostname:
      name: "{{ new_hostname }}"