How to modify the HTML formatting of an oEmbed link?

WP_oEmbed::data2html() has a filter, oembed_dataparse. You can use this to change the output, based on the extra data which is passed as the second parameter.

Something like this for example:

add_filter( 'oembed_dataparse', 'wpse17461_oembed_dataparse', 10, 3 );
function wpse17461_oembed_dataparse( $html, $data, $url )
{
    if ( FALSE !== strpos( $url, 'deviantart.com' ) ) {
        return $html . '<br/>Author: ' . $data->author_name;
    }
    return $html;
}