Yes in some cases a vet will come to your house to euthanize your pet for you.
That is especially true for large animals such as a horse that cannot be easily moved to a vet to be euthanized.
I remember as a kid we had a horse that got so severely injured that it had to be euthanized and my parents called a vet and they came to the house to euthanize the horse.
So you can get some vets to come to your house to euthanize the pet but you have to call around to a few vets before you will find one.
Some vets will come to your house to do the procedure and some may not.
Also you can get some vets to come to your house to check on the pet and treat them if possible.
But if the pet requires surgery or other medical procedures then you'll need to bring the pet to the vet.
If the vet comes to your house you'll usually need to pay an extra fee for a house call from a vet to see the pet or euthanize them.