Corrected entry: Nancy never gives any personal information in her letters to Hartigan, but he knows exactly how to get to her house when he gets out of prison. She couldn't have been listed anywhere under her own name, because Junior says he's been looking for her for years, and he would've easily found her.
Corrected entry: At the beginning of the movie when Bruce Willis is trying to find the little girl, his tie has some kind of pattern. When he gets to that dock place his tie is all white. Obviously he wouldn't stop his frantic chase for the girl to change his tie.
Correction: The effects the movie produces can easily alter patterns and such as they did with colors and blood. This is just another effect.
Correction: Nancy goes by her real name, as evidenced when Hartigan goes to the strip club and asks if anybody knows Nancy. Secondly Junior never seems to realize that Nancy is the girl he kidnapped and was going to rape when Hartigan came along and stopped him. It is quite possible and likely that Junior holding a grudge for what Hartigan did to him wanted to take everything that was close to Hartigan away from him. Once a week letters for 8 years would be a nice tip-off that somebody still cared for him. Finally, obviously Rourke didn't care if Nancy was alive or not because they let her live immediately after the kidnapping even though she could ID and give an account of what happened. Without her using her real name or giving a return address they had no real way of knowing it was Nancy who was sending the letters.