Update your code to assign your prototype to the Error.prototype and the instanceof and your asserts work.

function NotImplementedError(message = "") {
    this.name = "NotImplementedError";
    this.message = message;
}
NotImplementedError.prototype = Error.prototype;

However, I would just throw your own object and just check the name property.

throw {name : "NotImplementedError", message : "too lazy to implement"}; 

Edit based on comments

After looking at the comments and trying to remember why I would assign prototype to Error.prototype instead of new Error() like Nicholas Zakas did in his article, I created a jsFiddle with the code below:

function NotImplementedError(message = "") {
  this.name = "NotImplementedError";
  this.message = message;
}
NotImplementedError.prototype = Error.prototype;

function NotImplementedError2(message = "") {
  this.message = message;
}
NotImplementedError2.prototype = new Error();

try {
  var e = new NotImplementedError("NotImplementedError message");
  throw e;
} catch (ex1) {
  console.log(ex1.stack);
  console.log("ex1 instanceof NotImplementedError = " + (ex1 instanceof NotImplementedError));
  console.log("ex1 instanceof Error = " + (ex1 instanceof Error));
  console.log("ex1.name = " + ex1.name);
  console.log("ex1.message = " + ex1.message);
}

try {
  var e = new NotImplementedError2("NotImplementedError2 message");
  throw e;
} catch (ex1) {
  console.log(ex1.stack);
  console.log("ex1 instanceof NotImplementedError2 = " + (ex1 instanceof NotImplementedError2));
  console.log("ex1 instanceof Error = " + (ex1 instanceof Error));
  console.log("ex1.name = " + ex1.name);
  console.log("ex1.message = " + ex1.message);
}

The console output was this.

undefined
ex1 instanceof NotImplementedError = true
ex1 instanceof Error = true
ex1.name = NotImplementedError
ex1.message = NotImplementedError message
Error
    at window.onload (http://fiddle.jshell.net/MwMEJ/show/:29:34)
ex1 instanceof NotImplementedError2 = true
ex1 instanceof Error = true
ex1.name = Error
ex1.message = NotImplementedError2 message

This confirmes the "problem" I ran into was the stack property of the error was the line number where new Error() was created, and not where the throw e occurred. However, that may be better that having the side effect of a NotImplementedError.prototype.name = "NotImplementedError" line affecting the Error object.

Also, notice with NotImplementedError2, when I don't set the .name explicitly, it is equal to "Error". However, as mentioned in the comments, because that version sets prototype to new Error(), I could set NotImplementedError2.prototype.name = "NotImplementedError2" and be OK.

function InvalidValueError(value, type) {
    this.message = "Expected `" + type.name + "`: " + value;
    var error = new Error(this.message);
    this.stack = error.stack;
}
InvalidValueError.prototype = new Error();
InvalidValueError.prototype.name = InvalidValueError.name;
InvalidValueError.prototype.constructor = InvalidValueError;

Accoring to Joyent you shouldn’t mess with the stack property (which I see in lots of answers given here), because it will have a negative impact on performance. Here is what they say:

stack: generally, don't mess with this. Don't even augment it. V8 only computes it if someone actually reads the property, which improves performance dramatically for handlable errors. If you read the property just to augment it, you'll end up paying the cost even if your caller doesn't need the stack.

I like and would like to mention their idea of wrapping the original error which is a nice replacement for passing on the stack.

So here is how I create a custom error, considering the above mentioned:

es5 version:

function RError(options) {
    options = options || {}; // eslint-disable-line no-param-reassign
    this.name = options.name;
    this.message = options.message;
    this.cause = options.cause;

    // capture stack (this property is supposed to be treated as private)
    this._err = new Error();

    // create an iterable chain
    this.chain = this.cause ? [this].concat(this.cause.chain) : [this];
}
RError.prototype = Object.create(Error.prototype, {
    constructor: {
        value: RError,
        writable: true,
        configurable: true
    }
});

Object.defineProperty(RError.prototype, 'stack', {
    get: function stack() {
        return this.name + ': ' + this.message + '\n' + this._err.stack.split('\n').slice(2).join('\n');
    }
});

Object.defineProperty(RError.prototype, 'why', {
    get: function why() {
        var _why = this.name + ': ' + this.message;
        for (var i = 1; i < this.chain.length; i++) {
            var e = this.chain[i];
            _why += ' <- ' + e.name + ': ' + e.message;
        }
        return _why;
    }
});

// usage

function fail() {
    throw new RError({
        name: 'BAR',
        message: 'I messed up.'
    });
}

function failFurther() {
    try {
        fail();
    } catch (err) {
        throw new RError({
            name: 'FOO',
            message: 'Something went wrong.',
            cause: err
        });
    }
}

try {
    failFurther();
} catch (err) {
    console.error(err.why);
    console.error(err.stack);
    console.error(err.cause.stack);
}

es6 version:

class RError extends Error {
    constructor({name, message, cause}) {
        super();
        this.name = name;
        this.message = message;
        this.cause = cause;
    }
    [Symbol.iterator]() {
        let current = this;
        let done = false;
        const iterator = {
            next() {
                const val = current;
                if (done) {
                    return { value: val, done: true };
                }
                current = current.cause;
                if (!val.cause) {
                    done = true;
                }
                return { value: val, done: false };
            }
        };
        return iterator;
    }
    get why() {
        let _why = '';
        for (const e of this) {
            _why += `${_why.length ? ' <- ' : ''}${e.name}: ${e.message}`;
        }
        return _why;
    }
}

// usage

function fail() {
    throw new RError({
        name: 'BAR',
        message: 'I messed up.'
    });
}

function failFurther() {
    try {
        fail();
    } catch (err) {
        throw new RError({
            name: 'FOO',
            message: 'Something went wrong.',
            cause: err
        });
    }
}

try {
    failFurther();
} catch (err) {
    console.error(err.why);
    console.error(err.stack);
    console.error(err.cause.stack);
}

I’ve put my solution into a module, here it is: https://www.npmjs.com/package/rerror

I like to do it like this:

• Make use of name so toString() throws "{code}: {message}"
• Return same thing to super so it appears the same in the stacktrace
• Attach code to error.code as checking/parsing a code is better in code than checking a message, which you might want to localize for example
• Attach message to error.message as an alternative to error.toString()

class AppException extends Error {
  constructor(code, message) {
    const fullMsg = message ? `${code}: ${message}` : code;
    super(fullMsg);
    this.name = code;
    this.code = code;
    this.message = fullMsg;
  }
  
  toString() {
    return this.message;
  }
}

// Just a code
try {
  throw new AppException('FORBIDDEN');
} catch(e) {
  console.error(e);
  console.error(e.toString());
  console.log(e.code === 'FORBIDDEN');
}

// A code and a message
try {
  throw new AppException('FORBIDDEN', 'You don\'t have access to this page');
} catch(e) {
  console.error(e);
  console.error(e.toString());
  console.log(e.code === 'FORBIDDEN');
}

class NotImplementedError extends Error {
  constructor(message) {
    super(message);
    this.message = message;
  }
}
NotImplementedError.prototype.name = 'NotImplementedError';
module.exports = NotImplementedError;

and

try {
  var e = new NotImplementedError("NotImplementedError message");
  throw e;
} catch (ex1) {
  console.log(ex1.stack);
  console.log("ex1 instanceof NotImplementedError = " + (ex1 instanceof NotImplementedError));
  console.log("ex1 instanceof Error = " + (ex1 instanceof Error));
  console.log("ex1.name = " + ex1.name);
  console.log("ex1.message = " + ex1.message);
}

It is just a class representation of this answer.

output

NotImplementedError: NotImplementedError message
  ...stacktrace
ex1 instanceof NotImplementedError = true
ex1 instanceof Error = true
ex1.name = NotImplementedError
ex1.message = NotImplementedError message

This is my implementation:

class HttpError extends Error {
  constructor(message, code = null, status = null, stack = null, name = null) {
    super();
    this.message = message;
    this.status = 500;

    this.name = name || this.constructor.name;
    this.code = code || `E_${this.name.toUpperCase()}`;
    this.stack = stack || null;
  }

  static fromObject(error) {
    if (error instanceof HttpError) {
      return error;
    }
    else {
      const { message, code, status, stack } = error;
      return new ServerError(message, code, status, stack, error.constructor.name);
    }
  }

  expose() {
    if (this instanceof ClientError) {
      return { ...this };
    }
    else {
      return {
        name: this.name,
        code: this.code,
        status: this.status,
      }
    }
  }
}

class ServerError extends HttpError {}

class ClientError extends HttpError { }

class IncorrectCredentials extends ClientError {
  constructor(...args) {
    super(...args);
    this.status = 400;
  }
}

class ResourceNotFound extends ClientError {
  constructor(...args) {
    super(...args);
    this.status = 404;
  }
}

Example usage #1:

app.use((req, res, next) => {
  try {
    invalidFunction();
  }
  catch (err) {
    const error = HttpError.fromObject(err);
    return res.status(error.status).send(error.expose());
  }
});

Example usage #2:

router.post('/api/auth', async (req, res) => {
  try {
    const isLogged = await User.logIn(req.body.username, req.body.password);

    if (!isLogged) {
      throw new IncorrectCredentials('Incorrect username or password');
    }
    else {
      return res.status(200).send({
        token,
      });
    }
  }
  catch (err) {
    const error = HttpError.fromObject(err);
    return res.status(error.status).send(error.expose());
  }
});

The constructor needs to be like a factory method and return what you want. If you need additional methods/properties, you can add them to the object before returning it.

function NotImplementedError(message) { return new Error("Not implemented", message); }

x = new NotImplementedError();

Though I'm not sure why you'd need to do this. Why not just use new Error... ? Custom exceptions don't really add much in JavaScript (or probably any untyped language).

The following worked for me taken from the official Mozilla documentation Error.

function NotImplementedError(message) {
    var instance = new Error(message);
    instance.name = 'NotImplementedError';

    Object.setPrototypeOf(instance, Object.getPrototypeOf(this));
    if (Error.captureStackTrace) {
        Error.captureStackTrace(instance, NotImplementedError);
    }
    return instance;
}

NotImplementedError.prototype = Object.create(Error.prototype, {
    constructor: {
        value: Error,
        enumerable: false,
        writable: true,
        configurable: true
    }
});

This is fastest way to do it:

    let thisVar = false

    if (thisVar === false) {
            throw new Error("thisVar is false. It should be true.")
    }