Unify Array For JSON Encode?

I'm trying to json_encode my array I'm getting back so I can place it inside of a jQuery plugin for the data source. My issue is that I am using PDO to query my database to get back the array, but upon doing a print_r, I see that every name I'm getting back from my database is in its own array. How would I place all these results into a single array so that when I do my json_encode it is all in one readable string for the jQuery plugin?

Database Query (PDO) -

$query = "
           SELECT name
FROM  `clients` 
    ";      
    try 
    {
        $stmt = $b3->prepare($query); 
        $stmt->execute(); 
    } 
    catch(PDOException $ex) 
    {  
        die("Failed to run query: " . $ex->getMessage()); 
    } 
    $players = $stmt->fetchAll();

Example of the returned array upon doing (Note I have 8000 getting returned so I will only post the first 5 or so)

print_r($players);

 Array
( 

 [0] => Array
        (
            [name] => ! CBC.ZXR
    )

[1] => Array
    (
        [name] => ! marioxz
    )

[2] => Array
    (
        [name] => ! V v :]
    )

[3] => Array
    (
        [name] => !?!
    )

[4] => Array
    (
        [name] => !CU @ 1337
    )

So more or less, how would I unify my array, so that when I do

json_encode($players["name"]);

It will return back a single JSON string of the names mentioned above.

Edit

Current Code,

$query = "
       SELECT name
FROM  `clients` 
";      
try 
{
    $stmt = $b3->prepare($query); 
    $stmt->execute(); 
} 
catch(PDOException $ex) 
{  
    die("Failed to run query: " . $ex->getMessage()); 
} 
$playerNames = $stmt->fetchAll(PDO::FETCH_COLUMN, 0);

json_encode($playerNames);
var_dump(json_last_error());