Just to give a bit of the Childs perspective here I have kind of been in their shoes.
When I was born my mum and dad were married (at 17yo) so I took his name.
When I was 3yo they split up and he refused contact, they divorced and my mum changed back to maiden name but left mine.
When I was 6 she met my step-dad, 2 years later they had my brother who took his dads name and then a year later they married so everyone except me had same surname which confused me so I started using it unnofficially without any consent.
At 11 my name was legally changed and all my documents came through (NI card etc) which was fine until I was 15 and my step-dad vanished (literally). So they divorced,my mum went back to maiden name leaving my brother and I with the same surname.
When I was 18 my mum met and married another man who legally changed my brothers name and they went on to have children so all except me had the same name again. Then they divorced my mum took maiden name again leaving 3 children with one name and me with another.
Now I am 26 have a child of my own with DP who I've been with for 12 years and even if the issue had arisen I couldn't give my DS my surname because technically it is nothing to me :(, to me my name is literally worthless sometimes I think of it as a false identity because by all means of birth record I simply don't exist as the person I am so I do wish my mum had just given me her maiden name or left it as it was from birth. I was actually gutted that I felt I couldn't even put my surname as part of my DS name because it would link him to a family who would never meet him or even know if him.
DP's name sounds absolutely awful with my forename so even when we get married it won't be changed, but I guess there are more important things overall but all of this might be something to take into consideration before changing anyones name.
Sorry for such an epic post but this is a subject that does get to me.