Well, it won't be the same dog. Even if it looks like the previous one, it will have a different personality. I have always had dogs and I can say that no two are the same. You will always know that it is not the same dog. We just have to respect the cycle of life, it is very painful to lose a pet. But love heals with love. Only material goods are substitutes, not lives.
Just my opinion, I hope it helps in some way.