I've been speculating on that eagle for the whole arc now and I can't come up with anything that makes sense.
The first time we saw it was during "The Circle," when it flew overhead and warned Polly of the impending attack by the titular bodyguards. At the time, I assumed, "okay, omen of Artemis" - the eagle isn't the most prominent of her associated animals, but a deer wouldn't exactly be practical - and as Polly's midwife, Diana's indirect namesake, and one of the amazons' (and especially Diana's) chief patrons, Artemis sending an eagle to be her presence at the birth and protect the child makes a lot of sense.
That theory doesn't hold for the current arc, though. The events of "The Circle" demand that the eagle represents some benevolent patron. But Diana is pretty much *out* of those during this arc, when the eagle has been most prominent. It can't be Athena; she's dead at the moment, she didn't have the strength prior to her death, and she'd have sent an owl anyway. It can't be Kane; I'm reasonably sure they don't even have eagles in Hawaii, even if we hadn't seen the thing both before he ever knew Diana existed and after his death. It can't even be Ares, who would have still been her straightforward hateful enemy at her birth and who would have sent a vulture. Which leaves us back at Artemis again...
... but that really doesn't make sense either. Her place on Olympus, from Perez on out, has been a laid-back, basically obedient one, following the lead of the other patrons and certainly never challenging Zeus. She's been a complete non-player in the return of the gods so far - we haven't even seen her - which is just good continuity, since she disappeared during Rucka's run and Demeter took over her portfolio. Even before that, she'd have been the *weakest* of the Patrons, because unlike the others, she never reabsorbed her Roman aspect. Her suddenly turning out to be a player in this story on the level of Zeus and Ares (which something as thoroughly teased as the eagle would indicate) would seriously be almost as out of completely nowhere as Granny Goodness being behind Shamazons. (Not as stupid, mind, but nearly as out of nowhere.)
It's driving me batty. We've got Athena (loving and benevolent patron... at least by Batman standards... currently dead), Kane (kind of a hypocrite but nevertheless reliable patron, currently dead), Zeus (antagonist), and now Ares (troublemaking bastard), plus the other Olympians as a group (confused, uncertain, apparently uninvolved). And some unidentified sixth party who's apparently been looking out for Diana since her birth and has yet to make a move on this Genocide stuff apart from watching. AUGH I must have answers!