The use of private/custom nameservers is fully supported on cPanel & WHM systems, but must first be set up with your domain registrar. Here are the instructions for setting this up with GoDaddy.
To register nameservers with GoDaddy, follow these steps:
1. Under the Domains heading, select All Domains.
2. Locate the domain for which you wish to set up your nameservers.
3. Select the gear icon and select Manage DNS.
4. Select the Settings tab.
5. Under the Host Names setting, select Manage.
6. Select Add Hostname.
7. Enter the primary nameserver's name (for example,
ns1) in the Hostname text box.
8. Enter the primary nameserver's IP address in the IP Address text box.
9. Select Add.
10. Repeat steps 6-9 for your secondary nameserver (for example,
11. Select Save.
12. Click Edit Nameservers.
13. Select Custom.
14. Enter the full hostnames of your two nameservers (for example,
15. Select OK.
16. Select Save.
The interface processes your request and displays "Set Nameservers: Your request has been submitted. Changes may take a few moments to take effect."
More information is in our documentation here: