debug.yml

---
- hosts: application_servers
  remote_user: root
  become: true
  become_method: su

  vars_files:
    - vars/naming_convention.yml

  tasks:
    - debug:
        msg: "{{ vm_short_name }}"

    - name: blah
      file:
        state: directory
        path: /tmp/{{ hostvars[inventory_hostname]['vm_short_name'] }}
      delegate_to: database_master

# vim:ft=ansible

output.yml

PLAY [application_servers] ****************************************************************************************************************************************************************

TASK [Gathering Facts] ********************************************************************************************************************************************************************
ok: 
ok: 
ok: 

TASK [debug] ******************************************************************************************************************************************************************************
ok:  => 
  msg: app1
ok:  => 
  msg: app3
ok:  => 
  msg: app2

TASK [blah] *******************************************************************************************************************************************************************************
fatal:  FAILED! => 
  msg: |-
    The task includes an option with an undefined variable. The error was: 'ansible.vars.hostvars.HostVarsVars object' has no attribute 'vm_short_name'
  
    The error appears to be in '/home//ansible/playbooks//debug.yml': line 14, column 7, but may
    be elsewhere in the file depending on the exact syntax problem.
  
    The offending line appears to be:
  
  
        - name: blah
          ^ here
Failure message repeated for the remaining two hosts