The V5 form (log book) has a space to fill in your name and address as the 'New Keeper' the previous owner fills it in and you sign it. Then that part of the form is detached and handed to you. The previous owner sends the rest of the form off to DVLC . You keep the part you are given as proof of ownership until the new V5 arrives with your details on it. You just keep your part of the form until you get the new log book (V5) that is all you have to do, the previous owner has to send it to the DVLC.