i would split the method, maybe having something like:
``` 
def sender_name user
  message_object.anonymous && 'Anonymous' || user_name
end

def user_name
  user_is_owner?(user) && 'Me' || messager_object.sender.name
end
```

also, i see you use user in differents places, what it is ? is the relation to the message_object? or the current_user? there are some methods receiving it as parameter, maybe could be declared as an instance attr? not sure really :p