Yes, your technique is good, but you don’t need to wrap it if the root has not been peeled. Another way to store fresh ginger is to place it as is in the freezer. Remove it when needed and simply peel and grate the required amount. You can also peel and grate the ginger before you freeze it.
“I want to know how to store fresh ginger. Currently, I wrap it in plastic wrap and put it in the fridge, but I am not sure that’s the right way. Thank you.”