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.
Note: Deleting and recreating a plan will cause the Analytics reports to lose the data on the previous plan. Even with the same plan code being used, it's still considered a new plan that's just been created. When a plan is deleted, the only data stored for that plan is based around the customer data for all subscribers currently grandfathered on the plan. That would include the subscriptions, invoices, adjustments, and transactions data exports which would all list relevant data based on those customer subscriptions. The Analytics exports would be the only way to see the deleted plan's data outside of the accounts themselves.