Is it supermarket ginger? If so its Zingiber officinale. It may or may not grow because sometimes the rhizomes are treated with a growth retardant to prevent them from rooting on the shelf.
The rhizomes you can find in Asian markets are usually better about growing. If you plant ginger now, it will stay dormant because the genus Zingiber is naturally deciduous over winter. You should really wait until spring when its warm and the correct season for it to start growing
