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. Fire
2. Flame
3. Light
4. Bright
5. Lion
6. Tiger
7. Ginger
8. Red
9. Blaze
10. Ruby
11. Char(red)
12. Ember
13. Crimson
14. Maroon
15. Copper
16. Rose
17. Rust
18. Russet
19. Orange
20. Peach
21. Salmon
22. Glow(ing)
23. Cherry
24. Ruddy
25. Scarlet
26. Flare
27. Robin
28. Cardinal
29. Reddish
30. Blush
31. Carmine
Suffix:
January: step
February: foot
March: flame
April: cloud
May: whisker
June: heart
July: tail
August: leap
September: blaze
October: pelt
November: fur
December: storm
I'm Tigertail.