Er... You need to know that a site is composed of two "in-cloud" parts.
A data server where you store all the actual website stuff and a domain server which does some really weird things to get you a proper
www.mydomain.com rather than some creepy
www.me.aaa.com or aaa.blogspot.com or just simply 274.165.198.4 kind of an IP address!
In your current case, MMe provides you 20GB worth of data server space and a free aaa.me.com address. What they dont give you is a registered domain.
You must register a domain with whois.com or any other and then link that domain with MMe.