I miss a lot of the ongoing textual dialog in the ‘team say’ and ‘say’, mostly because I’m busy dying. Every once in a while someone will try to address me, and I’m likely to miss it.
I haven’t seen any really thoughtful designs for this part of the user interface (admittedly, I don’t play many games), but I do like the way HipChat works (which I use at work). People can be addressed with @, and there is a notification when your name is mentioned. So in game, we could have a visual/audio queue to draw attention. Typing @ provides type-ahead-auto-complete functionality too.