DNS server when transferring domain name(Kristofer Gafvert, April 5, 2006)
I host my own website and email server. I purchased and registered my domain name with Company A, but I have now transferred my domain name to another company. On the configuration website I am asked to specify a name server, what should I write?
I cannot give a short and definite answer (the IP address of the DNS server) to this question, because I obviously cannot know the DNS server of an unknown domain name. But I can explain how name resolution works in theory, and simplified, (it is a little bit different in practice and I do not want to complicate it) and tell you how to find out the IP address of the DNS server.
Say that an application (web browser or email client) needs to find the IP address of www.gafvert.info. The application puts the question to a local DNS recursor and the recursor asks one of the root servers the question: "What is the IP address of www.gafvert.info?". The root server replies with a delegation indicating: "I don't know the IP address, but I do know that DNS server 18.104.22.168 has information about the info domain". The local DNS recursor asks this DNS server the very same question and gets the answer: "I don't know the IP address, but I do know that DNS server 22.214.171.124 has information about the gafvert.info domain". A new request goes to this third DNS server, which answers with the IP address of www.gafvert.info.
The name server in your question is the name server for your domain (in the example above it is the name server for gafvert.info). You (or someone you have delegated the responsibility to) are responsible for this server. You set it up, and you configure it, hence nobody but you knows the IP address. As seen in the example above, the DNS server must be known by the DNS server for the tld (top level domain). This information (the IP address of your DNS server) is what you are asked to type.
When you register a domain name, you usually also get DNS hosting (because many tlds require that you specify a DNS server for the domain). So you may not even have known that before you transferred the domain name you had a DNS server for your domain. So now when you transferred the domain name, and cancelled the account with Company A, you also lost DNS hosting. Hopefully the company you transferred the domain name to also gives you DNS hosting with no additional cost.
So this is my answer to your question: Ask the company you transferred the domain name to, what the DNS server is. They should know.