Oh, I grasped the reason why Katniss steps up from the preview, but my impression still stands. The idea of a younger child having to face off against older children or adults in deadly struggles is not uncommon in children's stories;
Harry Potter practically revolves around the idea.
Primrose is eligible to compete, but she's the girl who doesn't have a chance, the tool used to showcase Katniss's bravery, self sacrifice, and dedication. That she's kind and will end up being a doctor doesn't change my feeling that Collins went looking for a name that conveyed passivity and the need to be sheltered and struck gold with
Primrose.
Like I said, everything I know about Hunger Games comes from the movie preview, the book jacket, and things other people have said, so I know I'm probably out of my depth here. I dislike the name for reasons that don't have anything to do with Hunger Games, and I'm sure they negatively influence my perception of the character. The information I have, though, makes me feel the author took advantage of the worst qualities of the name in naming
Primrose, looking for something sugary, babyish, ineffectual.