A) Logon to WHM on your new server. In WHM – look for the option to to add name servers. Now go ahead and input something similar like this:
B) Assign the IP addresses for your new name servers. Each name server must have its own IP address. A preferred option would be to have 2 different IP addresses from different subnets. Some domain registries will require this for failover purposes (assuming that there are 2 different DNS servers in different locations).
C) Once the name servers have been setup and IP addresses have been assigned you want them to be added to the DNS zone of your domain. This step is needed to have the actual name servers available for Internet usage. cPanel offers a very easy way to do this. Just click on the available button to add the entry/entries to the DNS zone file. You can double check this step by looking into the DNS zone file for your domain in WHM.
D) You are not done yet. If you have never used your own DNS servers before you will have to register your name servers at your domain registrar. In most cases an option to add DNS servers will be available in the domain control panel at your registrar. Once you have registered the domain name servers at your registrar it will take anywhere from 6 – 36 hours before they are available on the Internet.