title: Add column containing data frame name to a list of data frames
body: <p>If I have a list of data frames </p>
  
  <pre><code>my_list = list(data, data2, data3)
  </code></pre>
  
  <p>and I would like to add a column to each that is populated with that data frame's name</p>
  
  <pre><code>column1    column2    new_column    
  12         27         data
  27         987        data
  378        1234       data
  </code></pre>
  
  <p>, how would I go about this?  I would like all DFs within the set to retain their original names, but have it populate a column, as well.</p>
  
  <p>I have tried:</p>
  
  <pre><code>my_list = lapply(my_list, function(DF){
       DF$new_column &lt;- DF
  
       DF
  })
  </code></pre>
  
  <p>but it doesn't run through the list within the function.</p>
  
  <p>What am I missing?  Thanks</p>