My interpretation is that the Russian translator is fantastic, and is using the name to say something about her mother's character and their relationship. So she's someone who more often than most would use her full name to speak to her seriously.

In this case, she probably knows that she's giving her bad news, and her way of dealing with that might be to instinctively be *less* affectionate, perhaps to put Elizabeth into duty/soldier mode. She's expressing love, but not asking for pity, and speaking to her with her full name maybe signals that.