Extended - to provide more details based on some comments

The error

Error TS2306: File 'test.ts' is not a module.

Comes from the fact described here

17. Modules

This chapter explains how the built-in modules work in ECMAScript 6.

17.1 Overview

In ECMAScript 6, modules are stored in files. There is exactly one module per file and one file per module. You have two ways of exporting things from a module. These two ways can be mixed, but it is usually better to use them separately.

17.1.1 Multiple named exports

There can be multiple named exports:

//------ lib.js ------
export const sqrt = Math.sqrt;
export function square(x) {
    return x * x;
}
export function diag(x, y) {
    return sqrt(square(x) + square(y));
}
...

17.1.2 Single default export

There can be a single default export. For example, a function:

//------ myFunc.js ------
export default function () { ··· } // no semicolon!

Based on the above we need the export, as a part of the test.js file. Let's adjust the content of it like this:

// test.js - exporting es6
export module App {
  export class SomeClass {
    getName(): string {
      return 'name';
    }
  }
  export class OtherClass {
    getName(): string {
      return 'name';
    }
  }
}

And now we can import it with these thre ways:

import * as app1 from "./test";
import app2 = require("./test");
import {App} from "./test";

And we can consume imported stuff like this:

var a1: app1.App.SomeClass  = new app1.App.SomeClass();
var a2: app1.App.OtherClass = new app1.App.OtherClass();

var b1: app2.App.SomeClass  = new app2.App.SomeClass();
var b2: app2.App.OtherClass = new app2.App.OtherClass();

var c1: App.SomeClass  = new App.SomeClass();
var c2: App.OtherClass = new App.OtherClass();

and call the method to see it in action:

console.log(a1.getName())
console.log(a2.getName())
console.log(b1.getName())
console.log(b2.getName())
console.log(c1.getName())
console.log(c2.getName())

Original part is trying to help to reduce the amount of complexity in usage of the namespace

Original part:

I would really strongly suggest to check this Q & A: