windows 2000 logins

I have brand new win2000 workstations and brand new winadvanced server all with latest updates and service packs
how do i find out the correct name for the domain so when I try to login to new server i kow the right “domain name: AD is installed and when i first tried to pick a domain a got a probaly a DNS issue on the workstation I did add the computers to AD ises and computers or should I let them add themselves in. These workstations were in a NT 4.0 workgroup before this. Under server properties I can get three names for this computer one says name@…. the other is a pre windows 2000 name and the other is connected to DNS which is the real mccoy
thanks