Blizzard games are rated by the ESRB - but that covers the content made by the Developers that is available for review.
Player made content (chat and names) is governed by a separate Code of Conduct that is rather family friendly. That same policy covers the forums.
Here is the section on communications and naming
Blizzard games offer a fun and safe place to interact with one another across various game worlds. We encourage our players to cooperate and compete in our games, but crossing the line into abuse is never acceptable. If you come across a player violating the policies below, you should report them.
When participating in communication of any kind (chat, voice communication, group finder), you are responsible for how you express yourself. You may not use language that could be offensive or vulgar to others.
Hate speech and discriminatory language is inappropriate, as is any obscene or disruptive language. Threatening or harassing another player is always unacceptable, regardless of language used. Violating any of these expectations will result in account restrictions. More serious and repeated violations will result in greater restrictions.
Names are subject to the same rules established above. Any name the player has the ability to customize—such as player names, BattleTags, and guild names—must be appropriate and inoffensive. Any name that violates our standards or disrupts the community will be changed, and additional limitations may be placed on the offending account per our discretion.
Take note that acceptable names are determined by player reports and Blizzard’s decision, and role-playing servers may have distinct standards for using game-appropriate names.
The Forum Code of Conduct breaks out some of the specific things the mods action for in chat or names Forum Code of Conduct - Blizzard Support
And of course the EULA covers all of the games and forums. It has the details on ownership (Blizz owns the bnet account, characters, game code, items, sound files, graphics, etc etc.) cheating, and more.