I'm sorry, but it is not possible to transfer service to a new name. I suggest you follow the instructions for canceling here.
Once the service is cancelled, your replacement can re-order the service. To ensure Yahoo's computer doesn't think it's the same customer reordering the service (same address & phone number), I suggest the phone number be changed. That way she'll qualify for the benefits of the free trial period and it will also reduce the downtime between disconnection and reconnection.
Your replacement can arrange her own service by going here.
IMPORTANT: If you're thinking about letting your replacement just use the service in your name, you might want to reconsider. NTT and the internet providers have long memories. Every year one or two foreigners come back to Japan and, before they can get phone or internet service, have to pay off years-old bills dating back to a previous time living in Japan.