According to a Game Freak blog post (source), she was named after Junichi Masuda's daughter, who was born around the time of the Pokémon Ruby and Sapphire in Japan. This makes her an example of an Easter egg in the game (or hidden feature).
Some of the lines of her in-game text reveal facts about Kiri, which Junichi Masuda wanted to share in the game.
"Hi, what's your name? ... ... ... ... ... ... ... ... ... Okay. That's nice! My name is Kiri. My mommy and daddy named me that so I would grow healthy and warmhearted. That's what they wished. You can have one of these." "Kiri will give you this Berry, too! I really like it lots!" "I wonder what kind of wish is included in your name."
After talking to her at least once during the current day:
"Spring, summer, autumn, and winter. If you're born in springtime, do you like the spring, and if you're born in the summer, do you like the summer?" Yes: "Then Kiri was born in the autumn, so I love the autumn! Which season do you like?" No: "Oh... It doesn't matter... There's so much that I want to know..."