For the prefix, use the day you were born on. For the suffix, use the month. If you're not comfortable sharing your birthday, use a random date— today's date, holiday, etc.

Prefix:
1. Shrew
2. Mouse
3. Fox
4. Deer
5. Fawn
6. Buck
7. Badger
8. Raccoon
9. Rat
10. Mole
11. Vole
12. Quail
13. Possum
14. Coyote
15. Squirrel
16. Chipmunk
17. Rabbit
18. Bunny
19. Skunk
20. Weasel
21. Ferret
22. Beaver
23. Turtle
24. Skink
25. Snake
26. Frog
27. Toad
28. Fish
29. Crab
30. Trout
31. Bird

Suffix:
January: claw
February: fang
March: foot
April: strike
May: whisker
June: leap
July: tail
August: heart
September: catcher
October: pelt
November: step
December: fur

I got Bucktail.