The 'first' or given name in Japanese is 名前 (なまえ namae), and the 'last' or family name is 名字 (みょうじ myouji) or 性 (せい sei).
You probably already know that in Japan, the position of the 'first' and 'last' name (in Western languages) is reversed. So for instance, Ayumi Hamasaki is called 浜崎あゆみ (hamasaki ayumi).
The position does not change for non-Japanese names. So if your name is John Smith, you do not become スミス・ジョン (smith john), your name order stays ジョン・スミス. (You may notice the ・ betwenn the ジョン and スミス; a delimiter like that is usually used between the first and last names of a foreign name to show where which is which.
But what about the names of Japanese Americans or other people of Japanese origin? For instance, the recently named Secretary of Veterans Affairs, Eric Shinseki, is a Japanese American. Do Japanese people call him Shinseki Eric? No they don't - his name remains in the order it's given in English, which is also spelled out all in katakana (エリック・シンセキ). (According to Wikipedia Japan, the kanji for his family name is 新関, but this has not been used at all in newspaper reports about him.)
I think this is a reflection in a way of the way Japanese people who live in Japan think of Japanese emigrants and their descendants. Once they leave, they are essentially no longer Japanese. The become people of Japanese origin (日系人 にっけいじん nikkeijin), but no longer Japanese (日本人 にほんじん nihonjin). I can't imagine a 日系人 achieving success in another country and that being regarded in the same light as a 日本人's success (in the way the success of Barack Obama was embraced as an achievement by 'one of us' by the people of Kenya for example, even if he's only half-Kenyan by blood).
For instance, in the 1992 Winter Olympics (ok, I'm dating myself), a Japanese-American figure skater Kristi Yamaguchi (クリスティー・ヤマグチ) was a rival of a Japanese figure skater, Midori Ito (伊藤みどり); when Kristi Yamaguchi eventually took the gold medal, no one in Japan embraced it as an achievement in ethnic-pride terms. It was just an American winning.
