"My name is not Corinna."
Translation:Nomen mihi non est Corinna.
What you have is fine. The course contributors need to add all of the different variations to all of the different sentences individually by hand, so there are bound to be a number of oversights. Please flag it in-lesson next time and report "My answer should be accepted." You will then need to be patient because first it takes time for them to process the changes, then it takes time for those changes to roll out.
Although Latin is generally an SOV language, "esse" is a bit of a special case because it is a copular/stative verb and takes a subject complement, not an object. In this case, SVC is common, particularly with weak pronouns such as "is", which are more commonly used as demonstratives. So you could say "Is puer est" for "He is a boy", but it could be interpreted as "This boy is..." and therefore "Is es puer" would be more clear.
But the sentence you have is fairly clear and not easily misinterpreted, so it should be just fine. If you write that and it is rejected, please flag it and report "My answer should be accepted."
Because that's English syntax.
English is Subject-Verb-Object. Latin is Subject-Object-Verb. Granted, there is no object in this sentence, but they still follow the same general format. When the verb is a copula like "to be/esse", Latin can be Subject-Verb-Complement so that the subject and complement don't blend into each other. Latin syntax is somewhat flexible, but there are things it does not do. For example, the negation always comes before the verb, never after it. As a side note, "mihi" is not the genitive "my", it is the dative of possession "to me".
Here is a plain-English overview of what the cases are and how they work:
Latin cases, in English
Adjectives must agree in gender, number, and case with the nouns they modify, but they have their own declensions. Sometimes you get lucky and the adjective just happens to follow the same declension as the noun, but that is not a guarantee.
No, that's English syntax. In Latin, the noun generally comes before most modifiers (and "mihi" is the dative "to me", not the genitive "my"), and the "non" comes before the verb.
"Nomen mihi Corinna non est" is the most typical way, with the subject first and the verb last.
"Nomen mihi non est Corinna" is also acceptable, since "esse" is a copular verb and "Corinna" is the subject complement and not any kind of object.
Just like in English you have a certain syntax you can't just put words into any order in Latin, though granted it is fairly flexible.
Orders that work are:
Nomen mihi Corinna non est.
Mihi nomen Corinna non est.
Corinna nomen mihi non est.
Corinna mihi nomen non est.
Nomen mihi non est Corinna.
Mihi nomen non est Corinna.
Rae has some good replies in this comment section about the gammar, for example this one: https://forum.duolingo.com/comment/33904818?comment_id=39074899