Of course, but the identity of the children passes on to the father.
Japan has a definite unique social construct in which males are leaders, and as much as developed Japan is, there is still this social thinking that the woman is to be submissive to the man. It reflects Japan's inherent conservative social construct. Tho I do hope that there will be a legislative push to encourage greater opportunities for women to climb up, one has to recognize this reality.
A lot of professions, unfortunately are gendered. One for example is Nursing and Medicine. In Japan, majority of nursing students and professional nurses are still female, tho there are a growing number of males taking this professional career path. Medicine, on the other hand is masculine, as majority of Japanese who study medicine are men. Some fields that are still gendered include: Engineering, Military.