machine name in dual boot situation

I have a machine that dual boots between NT WS and W2K Pro. Should the machine name be different for the two operating systems? I tried using the same name for both and after logging on with the W2k box and trying to log on with the NT box, it wouldn’t let me on. After going into Server Manager on another box and clicking on my computer name, I got a message that the trust had been broken. I renamed my NT box and rejoined the domain but for now I’ll leave my W2k box off the network. Any enlightenment would be greatly apprececiated. Thank, Frank Manerchia