The name of a membership can be changed at any time. If it is changed though, it will be a global change - meaning any instance of that membership in the system will be changed to the new name (except for in Inventory). If anyone is connected to a membership that is deleted, they will no longer be connected to a membership. 

To rename or delete a membership, navigate to the Membership Programs editing page by hovering over Settings in the top right menu.

On the right side of the page, on the corresponding membership program that you want to edit, there are red links that say rename and delete. Use these buttons to make your edits.