If you wish to permanently close or delete your account, you can do so by closing your WordPress.com account. Your data on Gravatar will be deleted, so make sure this is what you want.
Account closure cannot be undone.
You will not be able to open a new WordPress.com account using the same email address for 30 days. This includes Gravatar, which means you can’t use the same email address for 30 days to create a new Gravatar account.
You will not be able to log in to any other Automattic Services that use your WordPress.com account as a login. This includes WooCommerce.com, Crowdsignal.com, IntenseDebate.com and Gravatar.com.
Once your WordPress.com account is closed, these services will also be closed and you will lose access to any orders or support history you may have.
If you have any questions at all about what happens when you close an account, please chat with someone from our support team first. They’ll explain the ramifications and help you explore alternatives.
There is an option to disable your Gravatar account if that is more suitable.
Gravatar Support