Beauregard asks you to give him a Wurmple if you catch one, so he can evolve it.
The Request
After you complete The Basics of Crafting, talk to Beauregard to accept this request.
Finding Wurmple
You can find Wurmple in the Horseshoe Plains area of Obsidian Fieldlands.
Completing the Request
When you go back to the village, talk to Beauregard and you can give him a Wurmple if you have caught one. If you have more than one, you will be able to select which one to hand over.
Beauregard will ask you which name you like best, so choose whichever one you prefer. You will receive 3 Dazzling Honey.