iamjoshellis

It would probably make more sense to use one of the filters described in:

As modifying the plugin will result in losing your changes if it’s ever updated. Something like this would display the screen name with link before each tweet:

add_filter('latest_tweets_render_tweet', function( $html, $date, $link, array $tweet ){
    $screenName = $tweet['user']['screen_name'];
    $twitterUrl = 'https://twitter.com/'.$screenName;
    return '<a href="'.$twitterUrl.'">@'.$screenName.'</a><p class="my-tweet">'.$html.'</p><p class="my-date"><ahref="'.$link.'">'.$date.'</a></p>';
}, 10, 4 );