I'm not a native speaker but here is my reason:

• la = of
• jina la mkenya = a name of a kenyan

That was my interpreation and this is accepted, so I assume it is correct. My feeling is that in Swahili you use complete different shortcuts in different situations from English. The translations Duolingo uses seem unnatural in many cases, but this is not bad, because we are learning the language and it helps to stick a bit with the literal translation.

Your translation is the correct answer. Duo's given answer is a word-for-word translation. It's technically not wrong, but it's not useful. I'll report.

Yes, in the genitival sense if nothing else.

Wewe ni mkenya :)