Randall is a student in Penelope's kindergarten class from the episode "Kindergarten Chaos!" He's a shy kid who's genuinely anxious around Pokémon, despite having nothing against them in theory.
When Ash and his friends bring their Pokémon to the school, Randall keeps his distance while the other kids are having fun. Even when Ash and Bonnie try to convince him that Froakie and Dedenne are harmless, he won't budge. Turns out he had a bad run-in with a Beedrill before, and that's enough to keep him spooked.
Things change when Team Rocket shows up posing as entertainers. They drag Randall onstage along with everyone else, but once their cover blows and everyone scatters, Randall ends up trapped in their getaway truck with Pikachu, Froakie, and Penelope's Sylveon. That's the turning point—stuck in there with them, he realizes they're actually friendly. The fear just melts away.
Once he gets over it, Randall doesn't hesitate to help Ash save the Pokémon and take down Team Rocket. Back at school, he tells the class how he saved Pikachu and Sylveon, and he's genuinely excited about calling them friends now. Ash confirms it, and before they leave, Randall even challenges Ash to a battle sometime down the road.
Content compiled by AnimeList.moe from publicly available sources.