Sure you could say this as a statement ""あなたは これを にほんごで なんていうか しっていますよ." but it would sound more natural if you were to put a "よ" on the end. I am sure you will understand that leaving a statement open like that could also be interpreted as a question. However saying this would require a special situation to use it correctly and would not be used very often. Think about it who are you going to say to "that they know how to say this in Japanese" , deffinately not a Japanese person I hope???
If you were to say in the third person "かれは これを にほんごで なんていうか しっている." That would be a phrase that would be more plausable.
I could add to that an even more simpler form "これ、なんていうん？"。 There are many diderent ways to say something, but you have to look at the context of what is being said.
There always have been these forms of speech, Teineigo, Kensongo, Sonkeigo, Kenjyougo and Keigo which are the five that you speak of. And Don't worry I know all about these and how difficult they are to use ,as I have to try to teach my "Japanese" staff how to correctly use it. But what I was pointing out was that in your sentence "あなたはこれを日本語でなんという（んです）か知ってます。" the （んです） is just plain wrong and should not be used. Yes you can roughly catergorise but what are you trying to say here "shiru" is a casual (and basic) word, and in more formal situationis, that word can be replaced by the many other words that are similar"
Regarding the あなたはこれを日本語でなんという（んです）か知ってます。 issue, I agree that you are plain right in your view. You can tell that it was written by someone who was on a rush eh? Thankfully I managed to put it within parentheses, which denotes that one can do without it and still sound logical.
During translation, I tend to stick with a more literal translation of what is asked to be translated, since what's natural can be subjective. It really depends on your method and style of translating. "あなたは これを にほんごで なんていうか しっていますよ" with the よ has the nuance that the speaker either confirming something that the listener already knows, or is telling the listener that you can/have the ability to know that you know how to say it in Japanese, as if the listener didn't know this already. Adding "yo" would also hint that the speaker already knows much about the listener's ability in Japanese
The first poster asks a translation of "you know how to say it in Japanese." Note the period at the back. あなたは これを にほんごで なんていうか しっていますよ with the "yo" would be more like "you know how to say it in Japanese!" As far as I can see, there is no such nuance in "you know how to say it in Japanese."
Think about it who are you going to say to "that they know how to say this in Japanese" , deffinately not a Japanese person I hope???
If the person whom you are asking is a Japanese speaking friend, perhaps you can use "これをなんというか知ってるんじゃないか。" I am sure the senseis here will correctly me if I am wrong. But this discussion is already digressing from the poster's original intention, since apparently "you know how to say it in Japanese." is a statement, not a question.
the masu form can be considered to be a form of teineigo, or polite speech. And perhaps I shouldn't add the word formal since there really is not a direct corresponding category for that in Japanese. There used to be teineigo, kenjougo, sonkeigo, but now there apparently are 5 categories instead of 3.
There always have been these forms of speech, Teineigo, Kensongo, Sonkeigo, Kenjyougo and Keigo which are the five that you speak of. And Don't worry I know all about these and how difficult they are to use ,as I have to try to teach my "Japanese" staff how to correctly use it. But what I was pointing out was that in your sentence
"Keigo" cannot be mentioned in the breadth as kenjougo and sonkeigo etc., since kenjougo and sonkeigo are really subcategories of keigo. Also, "kenjyougo" and "kensongo" are exactly the same thing, so it is impossible to list them together as if they are two different entities.
The five that I was referring to are: teineigo, sonkeigo, kenjougo, bikago, and teichougo. A site that you and the staff to whom you are teaching may find useful is:
敬語 - Wikipedia (in Japanese) under the section called "日本語における敬語表現". I wouldn't say that you are plain wrong, since, yes, wikipedia is not necessarily the ultimate authority on this matter, and may not be correct, if at all; but I'd be interested to read an article that explains your list of "Teineigo, Kensongo, Sonkeigo, Kenjyougo and Keigo".