Myth: Many surnames have a coat of arms.
Fact: Coats of arms are not attached to a surname, but rather to an individual. People with the same surname may be entitled to different coats of arms, or not have one at all, unless they can prove that they are directly descended from a legitimate male member of that line – or one is granted to them. Are you researching heraldry?
Here are some resources to start:
And just for fun, this website explores the real history, heraldry and family trees that inspire Game of Thrones. Warning: contains spoilers.