You can request account removal in your settings, here. Pressing the DELETE ACCOUNT button will send a confirmation request to the e-mail address associated with your GOG account. After confirming your wish through e-mail, your GOG profile will be permanently deleted within 14 days, during which you’ll be able to log in and access your owned content. Afterwards, the account's removal becomes irreversible.
Additionally, after an account has been deleted, it's not possible to restore its content (purchases and/or redeemed codes) on a newly created account, and you will not receive refunds for any purchases made on your account when it's deleted.