Wow players must provide their personal information when register a new wow account. All the information should be true. Otherwise, you can not modify any message about wow account when you need help from Blizzard representative. So, there is a contradiction in the information as it is sensitive to everyone including credit card number, email address. If you are worried about disclosing the information you have submitted, you'd better remove personal information when close wow account.
You can use the email which you have registered by wow account to email email@example.com to request a remove. The email must including the primary account holder's name, telephone number and date of birth.
You can request any additional removals that you think necessary. Blizzard keeps names, birth dates and email addresses on file to identify wow account holders. This information can be removed when you close a wow account, but it will require speaking with a customer service representative directly.
At last, you just need to wait for your response email that Blizzard email you with an address ending in @blizzard.com .A representative may call a listed contact number if further details are necessary.
The recommended is just value for situation that removes your personal information when you plan to close wow account. As a long-term players, everyone should ensure their information be real and completely.