How would you do that - do you spend all your day in the house? I don't think I have ever laid eyes on the person who delivers our free local paper, usually on a Thursday.
I also suspect that your paper-girl is not allowed to not deliver to a house on the basis of a conversation that has no record. Remember that advertiser pay their money on the basis of a set number of houses their advert (in a local paper) is delivered to. If the delivery person is making decisions not to deliver to a proportion of the properties I think there would be some sting questions being asked, and possibly a return of advertising fees if the number of 'non deliveries' becomes significant.
This would work for us. Someone delivers a local free paper every week so we know the delivery (in this case) boy - though the delivery person changes every couple of years or so. Of-course the deliveries are checked from time to time to ensure that as many copies as possible are distributed and not being dumped in a convenient bin.
There was a free fancy magazine, country house style, that used to be delivered - but, following a single complaint, the distributors decided to not continue delivering it to any of the houses in the area/estate - causing a certain degree of bad feeling.
Generally, there's not a lot that can be done about unwanted advertising being delivered especially if it isn't covered by the Mail Preference Service.