This is from the Wood Badge Administrative Guide page 27:
"All Wood Badge for the 21st Century courses utilize the traditional Wood Badge
patrol names, which were selected from animals found in North America: Beaver,
Bobwhite, Eagle, Fox, Owl, Bear, Buffalo, and Antelope. The order of patrol
names may not be changed and other patrol names may not be substituted."
The order is Beaver 1st, Bobwhite 2nd, etc, etc.