Establishment of a branch is classified as “foreign direct investment” under the foreign exchange law. You have to report related agencies or prior notification to Ministry of finance and the other related agencies.
If you wish to have a branch, you need to appoint a representative in Japan. The representative person is not required to be same as a representative of your home country’s representative, but in under Japanese law, the branch office representative has all rights about sales activities in Japan. And, among representatives of Japan, at least, one person should be living in Japan.