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. Gray
2. Ash
3. Mist(y)
4. Storm
5. Dove
6. Dusk
7. Ashen
8. Stone
9. Rock(y)
10. Cloud(y)
11. Slush
12. Dark
13. Pale
14. Boulder
15. Beech
16. Stoat
17. Rabbit
18. Tern
19. Pebble
20. Rain
21. Rubble
22. Shade
23. Slate
24. Smoke
25. Wolf
26. Dew
27. Dust
28. Goose
29. Larch
30. Robin
31. Soot

Suffix:
January: cloud
February: foot
March: shade
April: pelt
May: tail
June: fur
July: whisker
August: face
September: belly
October: feather
November: storm
December: heart

I'm Duskwhisker.