access parent object in javascript

You can't.

There is no upwards relationship in JavaScript.

Take for example:

var foo = {
    bar: [1,2,3]
}

var baz = {};
baz.bar = foo.bar;

The single array object now has two "parents".

What you could do is something like:

var User = function User(name) {
    this.name = name;
};

User.prototype = {};
User.prototype.ShowGreetings = function () {
    alert(this.name);
};

var user = new User('For Example');
user.ShowGreetings();

var user = {
    Name: "Some user",
    Methods: {
        ShowGreetings: function() {
            alert(this.Parent.Name); // "this" is the Methods object
        },
        GetUserName: function() { }
    },
    Init: function() {
        this.Methods.Parent = this; // it allows the Methods object to know who its Parent is
        delete this.Init; // if you don't need the Init method anymore after the you instanced the object you can remove it
        return this; // it gives back the object itself to instance it
    }
}.Init();