On bender this is the equivalent:
<p class="name"><?php _e('Name', 'bender') ?>: <a href="<?php echo osc_user_public_profile_url( osc_item_user_id() ); ?>" ><?php echo osc_item_contact_name(); ?></a></p>
As you can see, it's not the user's Name or Username what is used directly, but the Name specified when the ad was posted: osc_item_contact_name()
You could just change that for osc_user_username() if only registered users can post ads on your site.
Regards