How to display current user name in webform field?
You can alter the webform and put some and achieve this.

&lt;?php 
    function module_name_form_alter(&amp;$form, &amp;$form_state, $form_id) {   
   // module_name = your custom module name.
       if($form_id =='webform_name')
        // webform_name = your webform id
           //check condition for non login user
           if(!user_is_logged_in()){
            {           
             $form['submitted']['field_name']['#default_value']= 'anynomous';  
             // field_name = Field name        
            }
         }
    }

    ?&gt;


You also need to debug using dpm. Which helps you solve you problem easily.

I believe that you can also do this using Rules module. You also need to try for this.