Yes, dogs can eat hamburger buns.
They do not provide much in terms of nutritional value, but they are generally safe.
They might be even better for dogs than for humans, because they often contain other grains besides wheat, such as rye and oats.
These offer a lot of beneficial dietary fiber and nutrients that dogs need.
However, you should watch how many buns your dog consumes. Too many and you might run into digestive problems, as they are often full of preservatives and/or sugar.
There is generally nothing harmful about the buns, but some dogs might experience minor stomach upset from them.
As long as your dog eats this food in moderation, it should be fine.
