mysql_fetch_array() returns an array, the second parameter is the result type (accociative, numeric or both) and does not need a link identifier, therefore it should be:
$link = mysql_connect('localhost', 'root', '');
mysql_select_db('php', $link);
$query = "SELECT name FROM yeah WHERE song = 'lmao'";
$result = mysql_query($query, $link);
$final = mysql_fetch_array($result);
// Access the array values
echo $final['name'];
mysql_close($link);