allinye:

The idea of naming the houses after themselves, as the founders, was swiftly abandoned, because Webster felt a house called ‘Webster Boot’ had no chance of ever winning anything, and instead, each chose their favourite magical beast. For Chadwick, an intelligent but often temperamental boy, it was the Thunderbird that can create storms as it flies. For argumentative but fiercely loyal Webster, it was the Wampus, a magical panther-like creature that was fast, strong and almost impossible to kill. For Isolt, it was, of course, the Horned Serpent that she still visited and with which she felt a strange sense of kinship.

When asked what his favourite creature was, James was at a loss. The only No-Maj in the family was unable to consort with the magical creatures the others had begun to know well. Finally, he named the Pukwudgie, because the stories his wife told of curmudgeonly William always made him laugh.

Thus were the four houses of Ilvermorny created, and while the four originators did not yet know it, much of their own characters leaked into the houses they had so light-heartedly named.