Unless you name your character using your real name, or you put your real name as your Battletag, that information is not available to the game or forums.
Blizzard can be held liable for protection and control of Personally Identifiable Information (real name, address, phone number, financial info, email). They are required by law to disclose it to customers if that info was ever distributed - outside what we agree to in the Privacy Policy.
Our characters, in-game chat, battlenet account, items, etc - those are not ours and we have zero expectation of privacy with them. Never have. Harassment is not ok at all though - so people need to use the tools in place. Ignore the person, then if they go around Ignore, document the name/server they used, time, date, chat channel, nature of message. File an Ongoing Harassment ticket.