Of course. And so do Japanese living in the U.S., Germany or South Africa. Or Taiwanese in Spain or Canada. They live in another country, under its laws.

No Japanese in Japan, or Korean in Korea, or Chinese in China, or Taiwanese in Taiwan does put family name second. Nor the foreign media when speaking of them, be they leaders, politicians, artists, or plain citizens that make the news. And no media in the world refers to Xi Jinping as Jinping Xi. Or to Tsai Ingwen as Ingwen Tsai, Moon Jaein as Jaein Moon, etc.

Yet they will say Shinzo Abe instead of Abe Shinzo. Why this extraordinary exception ? Does not make much sense, if any. Translate all names or translate none.

Edit : Fun fact; if a foreign born person becomes a naturalized Japanese, they will have to adopt a Japanese name ( could be simply some sort of transliteration of their original name ) and it will be always legally displayed in Japanese order, family name first.