Your real name, address, phone number, ID numbers etc belong to you. That information is protected by various laws depending on the country.
Your Bnet account, char, char name, and char data, items, etc. all belong to Blizzard.
You have no expectation of privacy when using Blizzard’s platforms. They record and own everything we say using their forums, games, or chat programs.
Blizzard shall have the right to monitor and/or record your communications when you use the Platform, and you acknowledge and agree that when you use the Platform, you have no expectation that your communications will be private. Blizzard shall have the right to disclose your communications for any reason, including: (a) to satisfy any applicable law, regulation, legal process or governmental request; (b) to enforce the terms of this Agreement or any other Blizzard policy; (c) to protect Blizzard’s legal rights and remedies; (d) to protect the health or safety of anyone that Blizzard believes may be threatened; or (e) to report a crime or other offensive behavior.
2. Blizzard’s Ownership
A. With the sole exception of the Licensors’ Games, Blizzard is the owner or licensee of all right, title, and interest in and to the Platform, including the Games that are produced and developed by Blizzard (“Blizzard Games”), Custom Games derived from a Blizzard Game, Accounts, and all of the features and components thereof.
ii. All data and communications generated by, or occurring through, the Platform;
vii. All Accounts, including the name of the Account and any Battle Tags associated with an Account. All use of an Account shall inure to Blizzard’s benefit. Blizzard does not recognize the transfer of Accounts. You may not purchase, sell, gift or trade any Account, or offer to purchase, sell, gift, or trade any Account, and any such attempt shall be null and void and may result in the forfeiture of the Account;
What you pay for is access to online digital content owned by Blizz. Nothing more. Think of it like an amusement park pass.