I think this is actually a case of the writers forgetting the show's history. Either that, or Steffy is unaware of where the name Hayes came from.
And the whole situation with Carter is contrived - especially the idea that out of all the lawyers in LA, Eric would trust Carter to represent him in the divorce. It's right up there with new parents Steffy and Finn offering Paris to come live with them.
I guess if there was anything left in terms of psychological realism, it just went out the window this week.