How to freeze properties inside a contructor function in JavaScript

I'm trying to make the properties inside a constructor function immutable, i.e. the properties should not be altered either with a dot or bracket notation. E.g. I have my constructor function:

function OnceNamedOne() {
    Object.freeze(this.firstName = 'John');
    Object.freeze(this.lastName = 'Doe');
    this.fullName = this.firstName + ' ' + this.lastName;
}

I basically want to freeze the properties and hard wire their values as in the function. So, when an instance is created:

var me = new OnceNamedOne(); and when the value I try to change the property value, it should not work - that is the following should not assign 'John' to first name: me.firstName = 'John';.

How could I do this?