Another strong-willed type who will sort of challenge your leadership. I don't mean like Sten, I mean like if Alistair had had more of a spine. Like maybe it's not totally obvious that you should be the leader. I'd like to see disagreements and maybe even arguments instead of everyone always deferring to you.
Like someone posted earlier, a female who isn't crazy. Someone like...Mhairi.
But I also like the "dangerous" women, like Morrigan and Jack from ME2. So one of those, too, please.

An older, wiser companion is good too. I really liked Wynne in DAO, and even if someone like her doesn't make it in, someone who will actually ask you about how you're feeling every once in a while would be nice. I think the rest of the gang from DAO ask you like one question each (I remember Leliana asking about how it was living in the Alienage, Zev asked about your home while talking about Antiva, etc.), but then they go straight back to yammering about themselves. Meanwhile Wynne counseled you about adjusting to life as a Warden, your relationships, your duties and responsibilities, etc. It was nice.