Display WordPress commenter nice name

wp_get_current_commenter() returns an array, the entry 'comment_author' stores the name:

Array (
    ['comment_author']       => 'Harriet Smith,
    ['comment_author_email'] => 'hsmith@,example.com',
    ['comment_author_url']   => 'http://example.com/'
)

More information is available in the codex.

Update

To find the nice name, ask the DB:

/**
 * Searches the user table by display name.
 * @param string $display_name
 * @return object
 */
function get_user_by_display_name( $display_name )
{
    global $wpdb;
    $user = $wpdb->get_row( 
        $wpdb->prepare("SELECT * FROM $wpdb->users WHERE display_name = %s", $display_name) 
    );

    if ( ! $user )
    {
        return FALSE;
    }

    _fill_user($user);

    return $user;
}

// Usage:
if ( $userdata = get_user_by_display_name( 'Thomas Scholz' ) )
{
    print $userdata->user_nicename;
}

Caveat: Not tested. 🙂