Private name server associated with domain. Actually it is a DNS name server. Private Name Server contains the user’s own domain name of the user.
Example:
Ns1.yourdomain.com
Ns2.yourdomain.com
Basically If a user purchases a VPS based hosting or Reseller hosting then he/she might get a private nameserver. Or if any customer wants to make their own nameserver then can make it by adding NS & Child Nameserver records in their DNS management with the server IP address as a A Record.