Grey Wind was first of the direwolf pups found by Robb Stark, and the pup bonded immediately with the boy. Robb named him Grey Wind because he ran like the wind. Of all of the direwolves, Grey Wind is perhaps the greatest fighter, sitting at Robb’s side and ready to defend him in a heartbeat.
Grey Wind is Robb’s constant companion. While Ghost will roam and hunt for long stretches, Grey Wind is like a loyal escort who rarely leaves his lord’s presence. Shaggy Dog may be more ferocious, but Grey Wind quickly becomes more familiar with the way men fight. Grey Wind is accustomed to horses and war-craft, and fights fiercely alongside Robb on the battlefield — much to the dismay of the Lannister armies.
Robb named him Grey Wind after the Stark Banners. Theon makes a reference to it at one point because he finds it ironic that Asha also names her ship (a ship is to a Greyjoy what a wolf is to a Stark) Black Wind after her own families banners. That’s my favorite thing about Robb, his focus on his family.