I'm sorry, but you cannot tell the authority to use your name for the NTO if you were not the RK. You can tell them of your new contact details, but the NTO must by law be sent in the first instance to the person who was the registered keeper on the day.
You posted - There has been an issue with the keeper change so it's still not actually in my name (in process of being resolved).
Perhaps a NTO has been issued already, why don't you ask the council.
You have NO liability until you receive a NTO in your name.
As posted: 'if the previous owner does end up getting the NtO, he can submit reps that he is no longer the owner, and provide your name and address'. Then you deal with the NTO.