Give it a Primary DNS Suffix (you make make it up if you want) :)
Say it's called "ns1.publicdomain.com", add publicdomain.com as the Primary DNS suffix, it'll be good enough. Pretty much no operational impact in doing that.
And just in case, you set that under...
My Computer Properties
Computer Name
Change
More ...
You don't need to change the machine name at the same time.
Chris