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It is uncommon, but some sites actually work and run off their IP address, instead of a domain name. DNS, the domain name system, was created to give people an easy way to find a web site, but a domain name, typically maps to an IP address. An IP address is a set of numbers that is used to locate a web server. Technically you can have multiple domain names pointing to a single IP address.
In any event, if you are serving your IP to Google and not your domain name and want to switch that. All you need to do is follow the Google site move documentation, as you would with moving from one domain to another.
Google's John Mueller confirmed this in a Google Webmaster Help thread when someone asked about moving from an IP to a domain name.
I'd just follow the normal site-move guidelines, such as setting up 301-redirects and using the rel=canonical. Using the setting in Webmaster Tools is a great practice, but it's optional; it's not required for a successful move.
This is very rare but good to know.
Forum discussion at Google Webmaster Help.
