You can name your Icelandic Horse anything you'd like to name him, altho, generally, the Icelandic Horse has an icelandic-type name followed by the ranch name of the breeder (or owner, depending on who names him), with the word "from" in the middle.

"Fra" is the word in the middle for the horses from Iceland. Other countries use their own version of "from" (i.e. "von" or "från").

Therefore, a horse named Sokki, born in Iceland, might be registered as Sokki fra Kanastodum. If he was born in Germany, he might be registered as Sokki von Wiesenhof. If born in the US, he might be registered as Sokki from Ryder Ranch. If born in Sweden, he might be registered as Sokki från Gyllengården.