Selecting distinct values from a JSON

Underscore.js is great for this kind of thing. You can use _.countBy() to get the counts per name:

data = [{"id":11,"name":"ajax","subject":"OR","mark":63},
        {"id":12,"name":"javascript","subject":"OR","mark":63},
        {"id":13,"name":"jquery","subject":"OR","mark":63},
        {"id":14,"name":"ajax","subject":"OR","mark":63},
        {"id":15,"name":"jquery","subject":"OR","mark":63},
        {"id":16,"name":"ajax","subject":"OR","mark":63},
        {"id":20,"name":"ajax","subject":"OR","mark":63}]

_.countBy(data, function(data) { return data.name; });

Gives:

{ajax: 4, javascript: 1, jquery: 2} 

For an array of the keys just use _.keys()

_.keys(_.countBy(data, function(data) { return data.name; }));

Gives:

["ajax", "javascript", "jquery"]

I would use one Object and one Array, if you want to save some cycle:

var lookup = {};
var items = json.DATA;
var result = [];

for (var item, i = 0; item = items[i++];) {
  var name = item.name;

  if (!(name in lookup)) {
    lookup[name] = 1;
    result.push(name);
  }
}

In this way you're basically avoiding the indexOf / inArray call, and you will get an Array that can be iterate quicker than iterating object's properties – also because in the second case you need to check hasOwnProperty.

Of course if you're fine with just an Object you can avoid the check and the result.push at all, and in case get the array using Object.keys(lookup), but it won't be faster than that.