Does your dog remember your other dog that died?

Yes, the dog knows. Of course, the dog may not have the same emotional reaction that you do.

The night when my dog died, and I wrapped him in a blanket and laid him on the front porch overnight. The next morning I found my cat sleeping up next to him. I do believe the cat knew the dog was gone and was mourning over the loss of his friend. I do believe cats and dogs have some sense of loss.