If you show photos then there is a easy way to show the other user photo only
Add following code in your theme’s (child theme you are using one) functions.php

add_filter( 'fep_remove_own_avatar_from_messagebox', '__return_true' );

Or to show names of other user you have to use fep_message_table_column_content_author action hook. It needs some custom code. You need participants name then remove own name from them.