I've not had to enter a character name or anything in Brink - I have played campaign mode but only in offline mode. It wasn't until I played campaign that the game requested internet access. Do I have the chance to enter a character name or does it take my name from Steam?

I also entered my Psycho Pack DLC code into Steam with no result - can't see the items in the game.

Some of what you said seemed to not make sense to me.
But no you can't enter a name(to my knowledge), it should take the steam id