DNS registration problem?

[techeng at asu.edu]

Hello there:
        I have a question related to DNS registration and hope some guy
can help me out.
        The network configuration is
        network number:204.181.16.64
        mask: 255.255.255.224
        router: 204.181.16.65
        primary DNS: 204.181.16.82 dns1.mydomain.com
        secondary DNS: 204.181.16.81 dns2.mydomain.com


        I already registered "domain name" ( mydomain.com) on
www.register.com but they point my DNS to their DNS, like
dns4.register.com. When I asked them to change the DNS to point my DNS.

        They asked me
        (1) Give them both ip address and name of that DNS, like
204.181.16.82 and its name is dns1.mydomain.com.
        (2) "Register" these two DNSes. I do not understand what they
mean by registering? Do we have to pay additional money to register our
own DNSes?
        (3) Does it matter if we registered more than two names pointing
to the same ip address?

Thanks

Shen