"Your last name is Wang."
They do not. The idea is to have you learn it like you were dropped off in the country where no one speaks your language. People tend to remember their mistakes better then a lesson.
Duolingo is an absolutilly great way to learn but I recommend that it not be your only source of learning.
Stick with it.
No it doesnt. If you learn any other language they tell you the pronounciation AND the meaning. I did the whole numbers section without anybody telling me which word correspond with half the numbers. I am not telling that they should tell you everything, i get how duolingo works, but atleast the meaning of the words should be there, not just telling me, hey, this is a word in chinese, remember it.
In fact, they do teach the definitions for these words. They are at https://www.duolingo.com/skill/zs/Name/tips. I suggest that you check the tips out before you start a lesson.
If you are entirely new to Chinese, you can click on any part of the text with a dotted underline, & it will show an explanation/definition of the term/Chinese character. It introduces explanations to terms like "initial", "final", "tone", etc.
Guys, first thing you should know about Chinese is that Chinese characters(words) are way different than those of the Indo-European languages.
One single word can be used as noun, verb, adverb, or adjective without any changes both to its writting and pronounciation. As to the meaning, things are pretty tricky, let's put it on the back burner. Upon their charaterisics changing, ususally their meanings do not change, it is their positions in the sentence as well as their auxiliary words that do the modifying.
As in this case, e.g. Your last name is Wang. In the given answer 你姓王, 姓 functions as a verb here, however there is no corresponding verb in English. The literal translation would be “你的姓是王。" Note that in Chinese, 姓 only refers to one's last name. Since last name is family name, you don't "name" someone's family name, so you cannot translate 姓 to "name(neither verb nor noun)".
Same as other languages, literal translations are always awkward, at least colloquially. When talking about one's last name, like in this example, Chinese people would simply say 你姓王; 我姓王（My last name is Wang); 他/她姓王(His/Her last name is Wang). Duo's answer is perfectly correct and natural.
There are words that can mean completely different even if none of its charactors change.
Here comes a tricky one. 你是王，this can be "you are (the person whose last name is) Wang". 王 is the last name; or "you are the QUEEN", 王 is "the queen".
To make sense, I add a definite article "the" before "queen", which doesn't appear in the Chinese sentence. Please don't take it too literally, there is only one queen in a particular area after all.
As you can see, nothing but the meaning changed. I agree with @Renard_Urbain, Chinese is all about the context.^_^