When creating private nameservers, you will need to register a minimum of two.
To register private nameservers with GoDaddy, login to your customer account and then follow this guide.
1. Go to Domains and then My Domains.
2. Now select the domain you wish to register the private nameservers for.
3. Under the 'Host Summary' section click on 'ADD'
4. In 'Host Name' enter ns1
5. In 'Host IP1' enter your primary IP address.
6. Once you then click 'OK', your nameserver is registered
7. To register your second nameserver, repeat the above steps, substituting ns2 as the 'Host Name' and when entering your IP address increase the last number by one.
(eg. if your primary IP address is 188.8.131.52 then the IP address for ns2 will be 184.108.40.206.
Note: When creating private nameservers it may take up to 72 hours for these to propogate throughout the internet.