PHP变量inURL

I have a display page pulling from a database. With that I have a display function. I have everything working correctly, but I want to change the variable that is visible at the end of the URL, now it is from the 'id' column in my database and I would like it to be from the 'name' column.

This is my display function (included in another file)

public function __construct($rid, $table) {
/* Connect to Database */
    require('dbinfo.php');
    //$table=$this->table;  // Choose Table Optional
    $link = mysql_connect($databaseip,$username,$password);
    mysql_select_db($database,$link);
    $query = "SELECT * FROM $table WHERE rid=$rid";
    $result=mysql_query($query);
    $this->result = $result;
    mysql_close($link);

And the Get PHP in the header of the display page is as follows:

<?php
$rid = $_GET['r'];
require('func/recipe.php');
// Recipe Display Function
if (isset($_GET['r'])) {$recipe = new recipeObject($rid,'my table name');} else {
  header('location: SET URL');
}

?>  

And my database structure looks like this - https://www.dropbox.com/s/rfga1vl8miqcd9s/database.png?dl=0

So I missed this big time the first time around. My apologies. Here is what I found to work for the query portion. And should help with SQL Injections.

$termSafe = mysql_real_escape_string($rid);
$query = "select * FROM $table WHERE (name LIKE '$termSafe')";