Chat notifications should display at least where they come from. The notification could mention the room, where "xxx new messages in room yyy have been submitted". The only information "there are new messages in chat" is not enough.
Another important point is, that the default value (10) for chat notifications should be configurable. Most members never press the configuration button and wonder about all the notifications about new messages they receive. If I could change the default value to 0, it wouldn't occur.