Retrieving jsonp data with callback function
You can create a custom function called jsonp_decode with one argument to convert JSONP format to JSON format and return decoded JSON

function jsonp_decode($jsonp) {
  $jsonp = preg_replace('/^.*?\(/', "", $jsonp);
  $jsonp = preg_replace('/\);\s*$/', "", $jsonp);
  return drupal_json_decode($jsonp);
}


Then you can pull the "Name" from the result set as the following code:

$request = drupal_http_request('http://[local]/TemplateManager/GetRenderingStrategies?Wizard=false&amp;callback=jsonCallback');

$names = array();

$items = jsonp_decode($request);

foreach($items as $item) {
  $names[] = $item['Name'];
}

var_dump($names);