How to hide username displayed in code with Omega 3 theme
The theme function your trying to us is theme_preprocess_node, and you'r correct in replacing the Omega with [yourtheme].

The reason the function isn't getting called though is MYTHEME_alpha_preprocess_node should just be MYTHEME_preprocess_node. Alpha is part of the theme name, so if you remove it, the function should start working for you once you clear your cache.

EDIT ---------------------------------

Because drupal's template functions are still hooks, you can't just override the preprocess_node function, as omega's preprocess function is still going to run. However, what you can do is edit the $vars variable. Make sure you have the &amp; in the param ( ie function (&amp;$vars) ) so the vars is a reference.

From there, you should be able to modify the $vars['attributes_array']['class'] array and remove the unwanted class. 

So if you put something like this in your code, that should get you close to where you might need to be. 

function mytheme_preprocess_node (&amp;$vars){
    $count = 0;
      foreach($vars['attributes_array']['class'] as $class){
        if(substr( $class, 0, 7 ) === "author-"){
          unset($vars['attributes_array']['class'][$count]);
        }
        $count += 1; 
      }
}


EDIT 2 ============================

When I say remove the class from the var, I mean you should just be able to unset the variable (I updated my code snippet to show it inside the preprocess function).

You don't need to copy the whole of the omega_alpha_preprocess_node. What you actually are doing when you define your own theme_preprocess_node function is your telling drupal you would like to modify the variables for the node before it processes it. Because your working from a subtheme, the parent theme is still going to run it's own preprocess functions. So that class will always be added via omega. However, because your subtheme's preprocess function is downstream, it will get the &amp;$vars reference with that class already added to it. So instead of rewriting the function, all that is needed is to simply remove the class from the $vars variable that you received in your params.