Ok, calm down first. Take a deep breath.
Ok.
Now, a NT4 to Win2K3 migration is not that difficult, but some thought and planning needs to be done before you jump forward with this.
First off, go here:
http://www.microsoft.com/windowsserver2003/upgrading/nt4/default.mspx
(please remove any spaces)
And read the articles on a NT4-Win2K3 migration.
Now, as for domain names, when you upgrade one of the NT4 PDCs to Win2K3, you will have a choice of what domain name you want. It could be whatever you want it to be, admin.com, mycompany.com, mycompany.bob, etc. Whatever works for your company. (you will have to run DNS servers internally so the domain name resolves correctly.)
Now, with 2 NT4 domains, you do have a few choices on Active Directory forest structure. You could have 2 entirely different AD trees (admin.com and finance.com), and you could link the trees, making an AD Forest.
You could also incorporate the finance NT domain into the admin.com domain, making a singleAD tree domain.
You could also have the finance NT domain a Child Domain of the admin.com AD domain; it could be finananc.admin.com
So as you see, you have several choices. Hell, you could set up a single Win2k3 server as its own root domain (mycompany.com), then upgrade your admin NT4 PDC and make it a child domain of this empty root domain (making it admin.mycompany.com), and upgrade the finance NT PDC into another child domain (finance.mycompany.com)
Just think about what kind of setup is right for your company and go from there.
hope this helps