If a plan is deleted, existing subscribers will remain grandfathered in at the subscription plan terms that they agreed to at the time of signup, until they either cancel/it expires. Also, keep in mind that if you ever create a new plan with the same name as an old plan, the database will not know the difference, and you will see data for two different plans reported as the same plan. Last, if you ever want to make modifications to the plan or the user experience for anyone on those plans, you will not be able to do that. For example, adding an add-on option, or changing the emails that are sent to users on those plans. You will not have access to the plan entities to make those changes.
If you rename a plan, the new name will update across all of your subscribers.