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. Day
2. Night
3. Blue
4. Storm
5. Night
6. Fog(gy)
7. Cloud
8. Feather
9. Soft
10. Sky
11. Dawn
12. Light
13. Dusk
14. Bird
15. Sun
16. Cool
17. Eve
18. Horizon
19. Mist(y)
20. Rain
21. Smoke
22. Bright
23. Sunny
24. Breeze
25. Snow
26. Blaze(ing)
27. Flash
28. Dark
29. Dove
30. Robin
31. Raven

Suffix:
January: wing
February: storm
March: feather
April: flower
May: tail
June: whisker
July: cloud
August: step
September: blaze
October: blossom
November: pelt
December: pool

I got Foggycloud.

Thanks to relatedwords.org.