While animals are known to have a general idea of what they even look like, the ability to recognize oneself in a mirror is considered instinct. However, this question has many angles to explore.
A pet can be trained to understand and recognize their own reflection. This is called mirror self-recognition. Mirror self-recognition is a very basic form of cognition, which is used in many higher cognitive functions. To do this, the dog must first have a general idea of what it even looks like, and therefore has rudimentary MSR mechanisms.
How to train the ability?
Training a dog to identify its own reflection is not an easy task, but is entirely possible. Before starting this process you must find a mirror that the dog regularly looks at. If you do not have one handy, try buying one from a hardware store or other similar place.
Firstly, make sure that the surface of the mirror is clean and free from scratches. As well as this, you will need to put a small dot on the reflective surface of the mirror or on an inconspicuous area. This dot can be almost anything, such as a sticker or pen. You can set up the area of the mirror or where you will place this dot to be easy to see for the dog, but inconspicuous for everyone else. This way you can make sure that you are the only one who knows about it.
Next, approach your dog from behind and place yourself between your dog and the mirror. Let him look at himself in his reflection, and when he does do what is called "marking". If he does not, then try somewhere else. If the dog is a young puppy, you can start training at this point, but if your dog is older you should let him develop this ability on his own.
Conclusion
In conclusion, it is entirely possible for dogs to recognize their own image in a mirror. Through a process of careful training you can even train your dog to do so, although it must develop this ability on its own first. Furthermore, through this process you might learn something about the way your pet perceives the world and its capabilities. After it has learn you can reward it with a Custom Pet Blanket or a Custom Pet Mug.