I was with VPS Host A. When I wanted to have my domain name on the VPS from Host A, I simply entered the primary & secondary nameserver names at my registrars site and it was done. Host A's service was poor, so I've started with VPS Host B. They created nameserver names for me at Host B's DNS for my VPS. When I went to my Registrars site to entered these nameserver names, I was instructed to create an A record and a subdomain for each nameserver name. I don't understand why it was simple with the first set of nameserver settings but not the 2nd ones. The domain name for my first vps is different than my second vps. The nameserver names from Host A didn't include the domain name, for example Host A's were ns1.computer.com and ns2.computer.com and the nameserver names from Host B were ns1.mydomain.com and ns2.mydomain.com. Could it be that it wasn't easy the second time because the nameserver names included my domain name? Any ideas will be appreciated. It's confusing. Thanks.
Sounds like you were using your host's dns/nameservers which would've already been configured. Since you are using your own custom dns/nameservers you will need to configure them on your server.