Hello, jsc01! A very warm welcome to you!
Basically sum is intransitive meaning that it can not take a direct object. The compliment of sum is nominative here "Diana est dea lunae" as you rightly said. As in english we don't say "whom are you" but "who are you", yet if an object "whom did you choose to become goddess?"
I'm sure some one else (i.e Skylax) can explain that more clearly. I'm sure D'Ooge says something about this.
Welcome again and I hope you post often and with great eagerness