Changing a child’s name

Me and my partner are due to have a baby 2018 and the baby will have her last name . We have talked about getting married in future and I will also take her name. I have a child from a previous relationship and she has already said she would like the same name. The child has regular contact with the other parent and has the other parents last name. So I suggested the child double barrel their name. Which they agreeed. However the child is under 10 over 5 so would need to ask the other parent for permission chances are they will say no and the child will not say anything to the parent as the child is scared of saying anything g to them. So I want to know where i would stand with this? We are in the uk so it would be changed via deed poll and I can go through court to fight the other parent if they say no but that is costly