add a element to json array with Key/value using angular js

First of all, the object $scope.Json is not a JSON but a string. To get a JSON, you need to parse the string like the following:

$scope.Json = JSON.parse(<string>) ;

Second, your input is a peculiar JSON as it is an array with one element (in its turn having 3 elements. I guess you wanted this:

$scope.Json = JSON.parse({ Id:"5464", Class:"9", Rank:"4" }) ;

Once you have this, you can add the element you want as:

$scope.Json.Name = "Vicky" ;

Use Array map() method.

DEMO

var json = [{ Id:"5464", Class:"9", Rank:"4" }];

json.map(function(item) {
  item.Name = 'Vicky'; 
});

console.log(json);