Unlike products from other vendors, Apple Watch won't allow for custom watch faces, at least not at launch.
This has led to the typical angst seen before any major Apple product launch, where the culture of the company and the limits of resources clash with the expectations and imaginations of customers everywhere. Whereby everywhere, I mean the internet. John Gruber, writing for Daring Fireball:
I don't expect Apple to open up watch faces to arbitrary designs, even when the full Apple Watch SDK ships later this year. If they do allow third-party faces, I think it'll be through design partners hand-selected by Apple. (The Mickey face is arguably an example of this already.) The idea of fully-customizable watch faces is right in the sweet spot between the differing philosophies of Google (anything goes) and Apple (tightly controlled). Apple Watch currently offers 10 different faces, and most of those faces offer a lot of customization regarding which complications are visible, and the tint colors. It's a lot of fun to play with, but here's the thing: there is no way to set up a watch face that is ugly, or that doesn't look very Apple-Watch-y. Even the Mickey face looks like an Apple Watch Mickey face, because of the San Francisco font on the hour markers and the complications. That is by design, and I don't see that changing.
You'll be able to customize some of the built-in faces — Chronograph, Color, Modular, Utility, Mickey Mouse, Simple, Motion, Solar, and Astronomy — by changing the level of detail, the color, and/or the complications they support, but that's as far as it goes for now.
Back in September of 2014, as John points out, Apple Watch included two additional faces — Timelapse and Photos. The former showed animated landmarks like Big Ben. The latter let you pick your own image as a wallpaper behind the face. Both lit up a lot of pixels which, given how OLED displays work, were "expensive" in terms of battery life.
There's no ambient mode, as far as I know, yet implemented to reduce that cost. Which is why custom watch faces would likewise prove "expensive" right now, and for reasons beyond battery life.
There have been a lot of theories as to why it took until the second generation iPhone for third party apps — custom apps, so to speak — to ship. One of the most practical reasons is that it took so much time and effort for the team to ship the iPhone itself that there was nothing and no one left to even begin making an SDK. After launch, the team that had just finished one marathon of sprints had to immediately engage in another just to get the App Store ready for the next year.
Features are "expensive" when it comes to resources. Working on one means you can't work on another, not at the same time. It's en vogue for everyone to complain about software stability and lack of features in sequential breaths, of course, but it's not realistic.
Apple has only promised native watch apps for later this year, for example. Native code on the watch, at the very least, would seem to be a prerequisite for custom watch faces.
Culturally, though, I agree with John — it's hard to see Apple having a completely open watch face store for the same reason there's been no theme store to change iOS icons and interface elements, no SDK for the post-iOS 7 motion wallpapers, and on, and on.
It's easier to see a partner strategy where, like channels on the Apple TV or results on Siri, Apple makes deals for faces such as Mickey Mouse on a case-by-case basis. There's certainly room for more even in the existing watch face switching system. (Personally, I'd love a Superman watch face, though Disney owns Marvel and not DC, alas.)
That's probably not what people who like to tinker and customize want to hear, but anyone who likes to tinker and customize should be used to hearing just that when it comes to Apple. (The idea of policing the App Store for the kind of intellectual property rights violations that typically come with theme repositories, especially given the spotlight under which Apple operates, likely also holds incredibly little appeal.)
I try to never say never when it comes to Apple, because the company does change, and occasionally throws curve balls or calls for a Crazy Ivan. Perhaps one day there'll be custom watch face extensions, the way there are now custom keyboard extensions.
For right now, however, everything from battery life to engineering resources to company culture mean no custom watch faces at launch. And that might take a while to change, if ever.