That is a text field in your edit profile questions, so use your imagination, no limit.. 

Thanks buddy. That field should be limited to like 200 chars case who wants to see a user real name some like 10000 chats long as some spammers are doing. That field is not a post form but a short description about your self.

Real Name profile question is stored as "text" type of field in mysql.
According to mysql docs "TEXT is a string data type that can store up to 65,535 characters" .

If you are to add an addition in-script validator,  ow_system_plugins/base/controllers/join.php is a good place to start with. Take username validator as an example.