Renaming a Domain Controller's ComputerName
Petri has some advice for renaming your domain controller, and it's possible. There are lots of hooks throughout the DC into the domain's name. This article is simply for renaming your DC's computer name, as indicated in the title of this question: "Renaming windows 2003 domain controller?"
Really the best advice is to ensure that you have a second DC, and rebuild this machine once that second DC is able to take control. Certainly just power off your machine, ensure everything works on your domain using the second DC. That'll give you confidence that it's OK to go ahead and rebuild your first DC.
Heck, take a Ghost image of the machine that you want to rename in case things go sideways. If the re-naming project over the weekend doesn't give you good results, then you could reimage the machine and the users wouldn't be any wiser when they walk into work on Monday morning.
Renaming a Domain
You will encounter too many hidden hooks in Windows, Active Directory, and Exchange. You'll be paying the price in time wasted downstream, that I'd not even consider this option.