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. Tiger
2. Lynx
3. Leopard
4. Bobcat
5. Lion
6. Puma
7. Caracal
8. Cougar
9. Jaguar
10. Cheetah
11. Kodkod
12. Iriomote
13. Margay
14. Manul
15. Ocelot
16. Panther
17. Serval
18. Oncilla
19. Jaguarundi
20. Wildcat
21. Pallas
22. Pampas
23. Jungle
24. Sunda
25. Clouded
26. Marbled
27. Colocolo
28. Sand
29. Pantanal
30. Tigress
31. Lioness

Suffix:
January: tooth
February: leap
March: strike
April: claw
May: blaze
June: pelt
July: tail
August: fang
September: fur
October: foot
November: frost
December: step

I got Pumatail.

Sources
• https://wildcatsmagazine.nl/known-species-wild-cats/
• https://www.pumapix.com/wild-cat-species-world/
• https://www.wildcatsanctuary.org/education/species/
• https://www.wildcatfamily.com/wild-cat-lists/wild-cat-list-common-name-and-species-name/
• https://www.activewild.com/wild-cats-list/