"Beloved of Arlore, The Storm Comes. To stand fast against the flood is to drown, to bend is to live. The wise rabbit always knows where the nearest brambles are".
-1
Considering Eve would be executed if it was found out she were female, it may be in our best interests to bide our time before attracting unwanted attention to her.
"Beloved" isn't necessarily only used with people of the opposite gender, and so far nobody suggested that we should pull a "
Leda and the Swan" stunt with her (personally, I'd rather ship her with Suha).
For instance, when Jesus said to love each other, he didn't mean that people should strip down for a bacchanal, or even that married couples should cuddle more... Anyway, if the word disturbs you, just use "Chosen" or something, but know that at least in this context "beloved" is both gender-insensitive and (IMO) more powerful.
Besides, even if (or rather, when) she is found to be female, it'll be to her advantage to be publicly known that she's personally under the protection of a god and that killing (or even prosecuting) her would be a very, VERY bad idea.
EDIT: Nevertheless, you ended up making me bring it up, so... what would you think of having "Eve and the Rabbit" as a theme for poets, playwrights, sculptors and painters throughout the ages, and inflict one or more litters of (possibly long-eared) demigods on the Earth?
Zeus was one sneaky Casanova!