I know it might be a bit more of a headache for you but maybe you could change just your son's name for now and wait on your daughter? Or even change them both later.

Has she explained why she's so adamant about keeping her last name? I had my first name changed to its English equivalent when I came to the United States (I was 6, so close to your daughter in age) and I felt like this person with the weird foreign name was almost like some other entity and I didn't like the sound of the new name. Of course my parents didn't ask they just did and then they told me about it after.

I have no idea if that's what's going on with the last name but maybe it's something similar. Maybe your daughter isn't thinking of her last name as something that ties her to members of her father's family maybe she thinks of it as part of her identity?

Perhaps you can gently tell her you're a family and you'll all have the same last name but give her some time to process. I'm assuming there's no rush.