The code you show actually does not make sense. The class you want to test offers no way to the outside world to get these private properties back, so currently there is no use case for that class at all in production code.
But I suppose that class really contains at least one method that does make an API call to somewhere, using these two bits of information. You would test that the strings passed into the constructor show up in this call, because it is irrelevant whether or not they were stored in private properties, they must be present in the API call.
And to test this, you enter the world of mocking. There should be an object inside your api
class that does the actual communication. And this object will get a method call with these secret strings. You should configure a mock object that checks that these strings are correctly passed.
If you do, you can then refactor anything related to storing these strings. You can rename the variables, you can move them into other object - anything would be possible, with your test still staying green because they do NOT test the internal structures of your class, only the observable behaviour from the outside. The outside world only cares about that.
But if you really thing you must test private properties: Use Reflection to make them accessible inside your test. Or write a getter method to read them.