How to throw exception in Web API?

It's absolutely fine.

Alternatively, if you wish to provide more info (to allow, as you say, the client to distinguish from regular 404):

    if (test == null)
    {
         throw new HttpResponseException(Request.CreateErrorResponse(HttpStatusCode.NotFound, 
"this item does not exist"));
    }

This blogpost should help you understand WebAPI error handling a bit better.

What you have in your code snippet should work. The server will send back a 404 Not Found to the client if test is null with no response body. If you want a response body, you should consider using Request.CreateErrorResponse as explained in the blog post above and passing that response to the HttpResponseException.