Yes, it is possible your own dog could be depressed. It is not like they could tell you but a change in behavior might be the first sign. You must therefore be attentive to your dog. The easy signs ( like humans) are loss of appetite, excessive sleeping, tiredness, and even aggressive bizarre behavior.
I would suggest seeing your vet and getting some labs. There are treatments that can be used. These are not unlike some we suggest in humans. I would stay away from medications as there are many supplements and herbs that work.
Here are some simple things to do for your dog if he/she is depressed.
1. Increase attention to your dogs needs. Play more , cuddle more and kiss more I kiss my dog Chaplin, every minute I can
2. I would give him/her new toys that are mentally stimulating. Not the usual stuffed animal toys, but chew toys are better. I recently installed a Orb Round aquarium. It amazes me how Chaplin sits in front of the aquarium watching the fish swim by
3. Light therapy. I do not know a light pet light that is suggested. I do know in the summer Chaplin and I spend more time in the sun on the terrace and in the park.
I often think : WHO SAVED WHO