If you're after the 'name', why does your code snippet look like an attempt to get the 'characters'?
Anyways, this is no different from any other list- or array-like operation: you just need to iterate over the dataset and grab the information you're interested in. Retrieving all the names should look somewhat like this:
List<String> allNames = new ArrayList<String>();
JSONArray cast = jsonResponse.getJSONArray("abridged_cast");
for (int i=0; i<cast.length(); i++) {
JSONObject actor = cast.getJSONObject(i);
String name = actor.getString("name");
allNames.add(name);
}
(typed straight into the browser, so not tested).