Actually, 日 doesn't mean "morning" at all; it can mean "sun" or "day".
Also, a more accurate and helpful explanation was already posted further down, by Rebekah, which I've taken the liberty of copying for you here:
「Funfact: 本 can also mean "main" or "orgin" besides book. I thinks thats the meaning used in 日本, orgin of the sun. I.e. land of the rising sun」
I think the "Type what you hear" questions need to be reviewed for consistency. Some will accept kanji and reject the hiragana (like this one), while others will reject the kanji expecting only hiragana. I believe はじめまして was an example of the latter (rejecting 初めまして). There is no option to flag these questions as "My answer should be accepted" either, so I'm not really sure how to appropriately report these inconsistencies on a question by question basis.
Unfortunately it's an issue with the program that those in charge of the course can't fix. Duo can only accept oneanswer for listening exercises. This is obviously a big issue for a language like Japanese where there can be multiple ways of writing the same word. They know the issue exists. The best suggestion I have is to follow precedent of what Duo uses for the words. If they use hiragana for a certain word, then when you put it into the listening exercise you should use hiragana too.
When you say "I am an American/I am American" you have to say アメリカ
人, meaning "American person." You would have to do the same for 日本 and say 日本人 if you wanted to talk about being a Japanese person.
日本人です。 - I am a Japanese person/I am Japanese.
日本しゅっしんです。 - I am from Japan. (しゅっしん or 出身 meaning 'to come from.')