Generically speaking, using "computer name" rather than 'IP address' of a computer when installing Server Software of any kind is a good best practice to follow. If your network uses DHCP IP assignment, this will cause IP addresses to change potentially which would invalidate your original installation causing other issues. You may be using IP reservations or static IPs but changes in your network 'might' require your reservations or static IP's to be changed down the road. So to be safe, it is always a best practice to use the computer name rather than an IP address.
Regarding your other point, nothing special needs to be done to enable access to the NP web console other than following the installation procedures and configuration of NPrinting user accounts. You must also install the NP designer on each computer that you wish to design NP reports from.
If your NP designer computers are outside of your domain where NPrinting server is installed, this might introduce other firewall or networking challenges that should be reviewed with your Networking team. But keep in mind, if you can VPN to your NP server web console location, and see the report/'edit' button you should be able to edit or create reports.
If from your NP designer computer you are unable to telnet either the computer name or the IP address that you installed NPrinting with, then you may have a networking problem as suggested in the point directly above.