Prime Minister Shinzo Abe’s new cabinet, announced Wednesday, includes a highly touted minister's position created to drive the new version of his Abenomics growth program. But no one's quite sure what to call it.

The minister’s job will be to push forward Mr. Abe’s new economic policies, which will focus on fighting Japan’s declining birthrate and meeting the goal of expanding the economy by about a fifth. Mr. Abe has said meeting such lofty goals will require the involvement of all 100 million of Japan’s people; hence, the...