Update: The initial report that the new membership program is called "Nintendo Account" is inaccurate. Nintendo Account is the name for the new account system, but the actual service is called My Nintendo.
Original: During new Nintendo President Tatsumi Kimishima's first presentation to investors, we finally got some new information about the promised membership program that is planned to replace Club Nintendo and provide better connectivity between Nintendo devices. The membership service will simply be called "Nintendo Account," and it will connect to Nintendo hardware, mobile devices, and PCs. Nintendo will use a cloud-based data service to transfer game data between mobile games and console games.
Source: The Wall Street Journal