Hosting and Name Registering Questions


I just transferred my web hosting from ehost to Dreamhost. I also had checked off that I want to transfer my domain name registry to Dreamhost. But after thinking about this a little bit, I realized that I had already paid Network Solutions for 2 years of registering my domain name. Can I cancel my request to have it transferred to Dreamhost, and instead create a new domain name to be registered through Dreamhost for free, as outlined in my plan? Will I need to pay more money to have this second domain name registered if I keep my original domain name registered with Network Solutions?

Forgive me if I get some of the terminology mixed up, I do get a bit confused sometimes.

Thank you for your help.