Oh dear. Some depressing replies overnight.
Bee Nope, married or not the surname should be whatever they want it to be.
On threads like this people always start asking "but what do you people with double barrelled names do when they get married?" Hmmm let me see, they have lots of options - they could each keep both their surnames, one person could change both surnames to the other's, or one or both could keep one name and change the other. In Spain, everyone has two surnames, no-one changes their name after marriage, and children have one surname from each parent. The tradition is to pass on names from the male line but it doesn't have to be that way - you could give the child one or both of the grandmother's names, or just pick whichever combo you think works best.
"As someone who grew up with a double barreled surname (not through marriage) I had no choice when I came to get married I could either keep it or lose it all."
As explained above, you did have a choice. I've had two surnames since birth and when I got married, I decided to keep one surname and change the other surname to DH's. You did have that option too. (And FWIW our child(ren) will have both surnames.)