Forgot to add that it is traditional for the woman to take her husbands surname but it is not a legal requirement so she doesn't have to if she doesn't want to.
If you want to keep your own name or just take his, you don't have to do anything. If he wants to take your name or you want to double-barrel your surnames, either he changes his by deed poll before the wedding and you take it upon marriage, or you both change by deed poll after the wedding.