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. Primrose
2. Blossom
3. Daisy
4. Bloom
5. Rose
6. Dandelion
7. Tulip
8. Petal
9. Flower
10. Peony
11. Carnation
12. Daffodil
13. Stem
14. Lily
15. Iris
16. Orchid
17. Allium
18. Violet
19. Aster
20. Azalea
21. Poppy
22. Sage
23. Buttercup
24. Boneset
25. Comfrey
26. Holly
27. Thistle
28. Fennel
29. Lavender
30. Marigold
31. Foxglove

Suffix: tail
January: blossom
February: whisker
March: bloom
April: petal
May: pool
June: heart
July: leaf
August: flower
September: wish
October: patch
November: tuft
December: shade

I got Dandelionleaf.

Sources
• https://www.proflowers.com/blog/types-of-flowers