As I understand, you want your system to use a remote nameserver to do DNS queries.
If the ISP's nameserver is at IP address 10.1.2.3, then you need a line in /etc/resolv.conf like so:
As for your system having no name... You can assign a hostname to your system, but that name will not be visible to the outside world -- if you want a specific name visible to the world, you must arrange to have a name/IP address mapping added to DNS.
For example, if your ISP has the address isp.com and you want your system to appear as myserver.isp.com, you would have to have the ISP add a pointer to your system to their DNS server. On the other hand, if you want a domain name all of your own -- such as www.mydomain.com
-- then you need to register it with a domain registrar and then arrange for them to point that name at your server's IP address.