Don't you have to have oghren as a companion until after you deal with Branka?
Sure you can tell him to go away once his quest is done but you can also tell Morrigan to leave like a minute after you get her, so if Oghren doesn't count she doesn't either.
True, I was thinking more that Morrigan comes back to you anyway in the end, so you can never really get rid of her for good. But you're right, she does fall under the same circumstances as Oghren. I guess the only one you really really can't miss out on recruiting for the majority of the game is Alistair. And even then, only to a certain point, you can lose him too eventually. You just can't end the game completely alone, whichever way you go.
Even Dog is missable if you're not a human noble. Poor Ser Barkspawn, why would anyone kill or send him away. 