Yes, dogs do miss other dogs. While we are not able to know what the remaining dog in the household thinks, observations show that the dog would show some behavioral changes. Dogs do not think or have concepts of death & dying in a way people do but do exhibit similar signs of grieving.
What a grieving dog may exhibit are a loss of appetite, some social withdrawal, lethargy or sleeping more than usual. It will even vocalize to call out the other dog that has passed on, even searching places where the other dog would frequent.
What you can do if your dog is grieving is to give it love and assurance. Keep its stress levels down. It will move on with time.