Let's say you have a playbook named foo.yml, and the playbook contains the following. The important thing to notice here is that the playbook does not include the remote_user parameter.

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

Let's say John Doe runs this playbook, targetting server1.example.com.

[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 [store the stats of example.txt in the 'out' variable] 
ok: [server2.example.com]

PLAY RECAP 
server2.example.com    : ok=1    changed=0    unreachable=0    failed=0 

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 --user command line flag can be used to define the user that will be used when making an SSH connection to a managed node (e.g. the target system). 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 jane.doe -vvv

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

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

The --user option is often used in tandem with the --ask-pass flag.

ansible-playbook foo.yml --user john.doe --ask-pass