If I am not correct but if you do a search and type in Area51.gov on Google it is listed... Forgive me but is this registered? Or is this just a purposely listed domain?

There isn't anything listed.

Yes... But the name comes up in a search.

Yeah but there isn't any offcial Area 51 site

Certain domain names are preregistered to be sure that noone that isn't related to the specific name, agency and place can register it.

Since its a .gov domain name, it is not posible to registerer it publicly but only posible for the US Govt to register it internaly.