The word "pup" is used for the offspring of banana trees. The pups form as rhizomes off the main trunk. Once they have developed roots of their own, they can be dug up and planted as new banana trees. Don't take too many at once or it may cause the main tree to be unbalanced and fall over.
Small pups are called buttons.
After the banana fruit has been harvested, choose one pup to become the new main trunk and cut down the old tree.