I'm using LR 6 and recently noticed this problem more than once.
I first chose the images, pressed "x" to mark them as rejected, then went to Photo> Delete Rejected Photos. When I checked, they were still in their original folder. About a week ago, I had renamed images then moved them within LR to a new folder (clicked & dragged). While the new folder listed them under their new name, the old folder had them with the original name. What's going on?
[I'm on a Mac running 10.9.5.]
I’m confused about what you’re describing as happening: The names of the images won’t change when you move them between folders in LR and the images won’t reside in both places when you move them within LR, and deleting them from inside of LR won’t delete them from the original folder if they somehow do reside in two locations on your disk.