Listen to me you ignorant little *ahem*.
Rose will keep her title of Lady even when Atticus becomes Baron, because it's HER'S BY RIGHT OF BIRTH as the daughter of a Marquess. Just like Edith will keep Lady. It is HER'S BY RIGHT OF BIRTH as the daughter of an Earl. She will have Lady from the moment she goes "goo goo, I am a baby" to "now I am dead!"
She was born with it, has it by right, and will always have it. Nothing, unless it turns out she is illegitimate, can take that from her.
And Cora does. As wife of a lord, she becomes a lady. Lady Robert Crawley, Viscountess Downton on marriage, to be precise -- and I know that is correct and that you are wrong as all you have to do is look at Kate Middleton. She's a commoner... on marriage she became PRINCESS William of Wales.
The same applies here for Cora. She becomes Lady Robert Crawley, Viscountess Downton. And then becomes Cora, Countess of Grantham (because Violet's title was Violet, Countess of Grantham and she's now Violet, Dowager Countess of Grantham so the same applies for Cora.)
Pelham is Bertie's surname -- so Edith takes that on marriage, but Lady is hers by right so she's Lady Edith Pelham, Marchioness of Hexham (and whatever else Bertie is... he presumably has at least one lower title for their child to take when he's born as his courtesy title.)
So, in future, kindly know when you're wrong. I won't have to ask you to bow down and beg for forgiveness then will I?