Until now, I thought new SE sites can't get a custom domain. But, look at an Area 51 proposal: Startup Business. It's in beta. Now, click the visit button to visit the beta site. It has got a custom domain host, custom brand & description. How?
Right from your A51 proposal link in big bad bold letters:
This site was seeded with content from answers.onstartups.com, a Stack Exchange 1.0 site.
What's Stack Exchange 1.0?
Our first idea was Stack Exchange… call it Stack Exchange 1.0. We thought we’d make our software available on a SaaS basis, a.k.a. “white label Stack Overflow,” so that anyone could start a site on a new topic in exchange for money.