Pets become equal members of the household and are often treated like family, and when one has to be given up all other members of the household are affected.
One of the safest ways to give your pooch up for adoption is to have one of your friends or family members take it if possible.
Your dog will change its environment but it will be with familiar people and you will know that it is safe.
If this is not an option, have your vet try to find a home for your dog. This is a very common and usually very successful practice because veterinarians are surrounded by animal lovers who can’t resist the opportunity to expand their pack.
Most vets will ask the previous owners not to try and contact the dog’s new family to make the transition as smooth as possible, which is perfectly understandable. At least you’ll know for sure your pooch found a good home.