Six Direwolf puppies were left orphaned when their mother was killed by a stag. They were each adopted by the six Stark children, with whom they each formed an especially close bond. Their names are great inspiration for name your own pet. This post is spoiler free, if you want to know more about each, click the links to their descriptions at A Wiki of Ice and Fire.
Ghost - Jon Snow's direwolf. Ghost was all white, with red eyes. Ghost was the smallest at birth, but grew to be the largest.
Grey Wind - Robb Stark's direwolf. His fur was the color of grey smoke and he had yellow eyes.
Lady - Owned by Sansa Stark, Lady had grey fur and yellow eyes. She was the smallest of the litter.
Nymeria - Arya Stark's direwolf. She had grey fur and golden eyes. She was named after a legendary Queen.
Shaggydog - Rickon Stark's direwolf. He had black fur and green eyes. He was sometimes just called Shaggy.
Summer - Bran Stark's direwolf. He had silver-grey fur and yellow eyes.
For more inspiration, check out my list of the Dragons of Game of Thrones.