It is certainly a strange request, but it makes perfect sense, at least grammatically. In fact, that's exactly the kind of sentence Duo is usually so fond of. Is nennen often used to mean sagen? I would've gotten the right translation if sagen were used, but nennen to me means "Call me by your name, rather than mine."
According to PONS, nennen jdn etw would be 'naming someone something' (in your hypothesis, naming me your name, so to speak). But nennen jdm etw, like in the original sentence, would be 'naming something to someone' (in the sentence, naming your name to me, i.e. Telling me your name). Not sure if it makes any sense.: p
"Wirst du mir deinen Namen nennen?"
Think of nennen not as 'to call a name' but as 'to make known', like, "let's call(name/make known) the relationship what it was, a mistake".
Look at it this way... "Wirst du(will you) nennen(make known) mir(to me) deinen Namen(your name)?"
No, here we have the case called nominative, the case for subjects of a sentence. Sure "was" is here already the subject, but in sentences with "sein" as verb (ich bin, du bist, er ist,...) and no preposition we have to use nominative.
- Was ist dein Name.
- Dein Name ist "Was".
- Du bist ein Schüler.
- Ein Schüler bist du. ~~> We are not able to tell anybody what the subject of the sentence is, so we use for both (for "Schüler" and "du") nominative. the same in the example with "was" and "Name".