There we go, you've finally got to the truth... You do think it's fair for her to give up her name. You want her to take DS's name.
Presumably you took DS's father's name?
What this comes down to is she wants to do something that differs to what you did. And you're not going to have the same name as her child.
I think double barrelling is the easiest option, in a way. Both people keep their name (sort of) so professional qualifications, degrees etc, can be more easily linked. There's an equal amount of inconvenience.
But if the double barrelling really is awful...
Could both names blend into one name? Does that work?
And if not, brand new name? That way it's an absolute pain for both of them, so it feels equal and fair.
Whatever they do, they're going to make different choices to you. You made a decision when you got married. It was your decision. If they do something else, it doesn't make your decision wrong.
Times are different, and their values are different. Plus, they're not you.