Can't get simple if / else statement to work

I am searching a table in my DB to return a tick if a name matches a $_GET['name'] variable that I have passed in the URL.

I want a tick displayed if the name exists and a cross if it does not.

The purpose is to populate a rota / timetable of availability.

The code I have so far;

<?php foreach($rota_sun as $rota_sunday): ?>
                            <?php if(strpos($rota_sunday['person_name'], $_GET['name']) !== false) { ?>
                                <span style="color:green; font-size:22px;"><i class="fa fa-check" aria-hidden="true"></i></span>
                                <?php } else { ?>
                                <span style="color:red; font-size:22px;"><i class="fa fa-times" aria-hidden="true"></i></span>
                                <?php } ?>
                            <?php endforeach; ?>

My code for the query is;

$query = "SELECT
                rota_sunday.id AS rota_id,
                rota_sunday.person_id,
                rota_sunday.person_name
            FROM rota_sunday WHERE rota_sunday.person_name = '$_GET['$name']'
        "; 
    try 
    { 
        $stmt = $conn->prepare($query); 
        $stmt->execute(); 
    } 
    catch(PDOException $ex) 
    { 
        die("Failed to run query: " . $ex->getMessage()); 
    } 
    $rota_sun = $stmt->fetchAll(PDO::FETCH_ASSOC);

My table contains three rows;

1. id
2. person_id
3. person_name