It made sense at the time--Darkseid was not just a villain rumored to be at the heart of Warner's planned Justice League film--he was the only villain discussed, showing up in numerous different rumors and leaks to different sites from different sources. And the recent redesign of the character for the New 52 put the omega front and center in a way that his previous costumes had not.
But since the Justice League script went up in smoke, and the new Warner CEO seems a bit less committed to film than his predecessor, a couple of sites have claimed their sources never really believed that Man of Steel was designed as a launchpad for a broader DC Universe, and so that a connection between the two villains was anything but a given.
Okay--fair enough. So what are our best guesses for the logo?
We'll just get this out of the way; we're still not totally sold on a lack of connection between the two. We're probably wrong, but when has that stood in the way of some fun speculation?
It almost seems as though the logo might not be an omega at all, but rather a stylized "U," not unlike the one Ultraman wears in JLA: Earth Two. It's askew, rather than straight on, but that makes sense in the context of filmmakers trying to craft a more realistic film universe where these are aliens who had no idea what written English looks like.
It makes sense that DC would shy away from the actual name Ultraman, which for copyright purposes is probably not something they can use on merchandising since there are other characters, arguably some better known, in popular culture who use the name. Still, using a similar logo and trademarking it might provide DC with merchandising opportunities while giving Zod a somewhat appropriate logo to boot.
After all, to the average non-comics-reading viewer, Zod really is a pretty close match for an "Evil Superman."
A perversion of the House of El's logo
It could be Zod thumbing his nose at Kal-El and his family, given that if you look at it the right way you can certainly see an "A." That said, it's recognizable as an S, not as the House of El's logo, so this one might be a bit of a stretch. Still, we've seen any number of characters over the years--from Bizarro to Superboy Prime--who took on an altered, damaged or otherwise bastardized version of the Superman crest to reflect their status as the broken mirror into which Superman can look to see his fears.
Depending on the relationship Zod has with the House of El, it wouldn't be outside of the realm of possibility for him to do that--especially if they retain the Donner version, where he's got a personal score to settle with Jor-El that's been driving him for years. That seems less likely, though, as this version of Zod seems a bit more in line with the Geoff Johns-written version who just wants a new planet to take over (is that so much to ask?).
Another logo they could be hoping to homage without actually using directly is the shield worn by Superman in the popular Elseworlds story Superman: Red Son. Written by Kick-Ass co-creator and Fox Marvel maven Mark Millar, the story is one of only a handful of Superman stories that really stand out in the last fifteen years or so, and was popular enough to become a motion comic that DC sells via digital outlets and the Warner Archive.
Of course, When you look at all the prongs on that logo, it looks a bit more like Faora's logo than Zod's, but we digress...
This is probably the most likely scenario--that it's just Zod's family crest on Krypton, per the Man of Steel version of the mythology. It doesn't particularly look like the letter Z, and it doesn't look like the logos used in the comics I've read or on Smallville--but that doesn't mean they couldn't have just decided that none of those fit the mood they were trying to establish in the film.
Probably, it's something a graphic designer came up with, and any similarity to these other things mentioned above is incidental or based on what s/he used as inspiration.