Domain Name Read here to understand more on Domain Name.
Many countries do allow foreigner to register their domain name.
Fine example are .TO, .ST, .CC and many other domains. On the other hand, certain countries will require you to have physical presence in that countries before you are allowed to register those domain name. Malaysian Domain Name and Singapore Domain Name are fine example of countries that require you to have physical presence before you can register their domain name. Yes, we can host domain name registered in any part of the world in your server. With the domain, you can house your web site in any Internet server with any ISP of your choice.