If you're sure that you wish to delete your account, contact GOG.com Support team. After verifying that you are the account's owner, they will initiate the deletion procedure.
Please keep in mind that account deletion is irreversible. Additionally, after an account has been deleted, it's not possible to restore its contents (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 is deleted.