There are 5 pups. One for each of the stark children. The Direwolf is the sigil of your house. They were meant to have them.
Kneel before me, lay your sword at my feet, pledge me your service, and you'll rise again as Jon Stark, Lord of Winterfell
You can't get any worse
Lady Stark thought it might insult the royal family to seat a bastard in their midst.