Let's say you have a playbook that does not include the remote_user parameter.

---
- hosts: all
  tasks:
  - name: demo
    stat:
      path: /path/to/example.txt
    register: out
...

Let's say john.doe runs this playbook.

[john.doe@ansible1]# ansible-playbook foo.yml -i server1.example.com,

Running this playbook should return the following. Notice the output does not identify that john.doe made the SSH connection.

PLAY [all]

TASK [demo] 
ok: [server1.example.com]

PLAY RECAP 
server1.example.com    : ok=1    changed=0    unreachable=0    failed=0 

The ansible_user_id variable can be used.

- hosts: all
  tasks:
  - name: store the stats of example.txt in the 'out' variable
    stat:
      path: /path/to/example.txt
    register: out

  - debug:
      var: ansible_user_id
...

Which should return the following.

ok: [server1.example.com] => {
    "ansible_user_id": "john.doe"
}

Or, the -vvv flag can be used to include some SSH output.

[john.doe@ansible1 ]# ansible-playbook foo.yml -i server1.example.com, -vvv

The following should be included in the output. In this example, "none" means that the user that invoked the playbook will be the SSH user.

<server1.example.com> ESTABLISH SSH CONNECTION FOR USER: None

The remote_user parameter can be used to define what user will be used when making an SSH connection to a managed node (e.g. the target system). In this example, user jane.doe will be used in the SSH connection. Now, when john.doe invokes the ansible-playbook command, jane.doe will be the user that makes the SSH connection. 

---
- hosts: all
  remote_user: jane.doe
  tasks:
    - name: store the stats of example.txt in the 'out' variable
      stat:
        path: /path/to/example.txt
      register: out

Now, when the playbook is invoked with the -vvv flag, jane.doe is identified as the SSH user.

<server1.example.com> ESTABLISH SSH CONNECTION FOR USER: jane.doe

The --user command line flag will take precedence over the remote_user parameter.

[john.doe@ansible1 ]# ansible-playbook foo.yml -i server1.example.com, --user jack.doe -vvv